Constraining dark energy with SNe Ia and large-scale structure

a rXiv:083.3292v4[astro-ph]1J ul28arXiv:0803.3292How to Distinguish Dark Energy and Modified Gravity?Hao Wei ∗Department of Physics and Tsinghua Center for Astrophysics,Tsinghua University,Beijing 100084,China Shuang Nan Zhang Department of Physics and Tsinghua Center for Astrophysics,Tsinghua University,Beijing 100084,China Key Laboratory of Particle Astrophysics,Institute of High Energy Physics,Chinese Academy of Sciences,Beijing 100049,China Physics Department,University of Alabama in Huntsville,Huntsville,AL 35899,USA ABSTRACT The current accelerated expansion of our universe could be due to an unknown energy component (dark energy)or a modification to general relativity (modified gravity).In the literature,it has been proposed that combining the probes of the cosmic expansion history and growth history can distinguish between dark energy and modified gravity.In this work,without invoking non-trivial dark energy clustering,we show that the possible interaction between dark energy and dark matter could make the interacting dark energy model and the modified gravity model indistinguishable.An explicit example is also given.Therefore,it is required to seek some complementary probes beyond the ones of cosmic expansion history and growth history.PACS numbers:95.36.+x,04.50.-h,98.80.-kI.INTRODUCTIONThe current accelerated expansion of our universe[1,2,3,4,5,6,7,8,9,10]has been one of the most activefields in modern cosmology.There are very strong model-independent evidences[11](see also e.g.[12])for the accelerated expansion.Many cosmological models have been proposed to interpret this mysterious phenomenon,see e.g.[1]for a recent review.In theflood of various cosmological models,one of the most important tasks is to distinguish between them.The current accelerated expansion of our universe could be due to an unknown energy component (dark energy)or a modification to general relativity(modified gravity)[1,13].Recently,some efforts have focused on differentiating dark energy and modified gravity with the growth functionδ(z)≡δρm/ρm of the linear matter density contrast as a function of redshift z.Up until now,most cosmological observations merely probe the expansion history of our universe[1,2,3,4,5,6,7,8,9,10].As is well known,it is very easy to build models which share the same cosmic expansion history by means of reconstruction between models.Therefore,to distinguish various models,some independent and complementary probes are required.Recently,it was argued that the measurement of growth functionδ(z)might be competent, see e.g.[13,14,15,16,17,18,19,20,21,22,23,24,25,47,48,49,50].If the dark energy model and modified gravity model share the same cosmic expansion history,they might have different growth histories.Thus,they might be distinguished from each other.However,the approach mentioned above has been challenged by some authors.For instance,in[26], Kunz and Sapone explicitly demonstrated that the dark energy models with non-vanishing anisotropic stress cannot be distinguished from modified gravity models(e.g.DGP model)using growth function. In[27],Bertschinger and Zukin found that if dark energy is generalized to include both entropy and shear stress perturbations,and the dynamics of dark energy is unknown a priori,then modified gravity[e.g.f(R) theories]cannot in general be distinguished from dark energy using cosmological linear perturbations. Here,we investigate this issue in another way.Instead of invoking non-trivial dark energy clustering (e.g.non-vanishing anisotropic stress),it is of interest to see whether the interaction between dark energy and cold dark matter can make dark energy and modified gravity indistinguishable.In fact,since the nature of both dark energy and dark matter are still unknown,there is no physical argument to exclude the possible interaction between them.On the contrary,some observational evidences of this interaction have been found recently.For example,in a series of papers by Bertolami et al.[28],they show that the Abell Cluster A586exhibits evidence of the interaction between dark energy and dark matter,and they argue that this interaction might imply a violation of the equivalence principle.On the other hand, in[29],Abdalla et al.found the signature of interaction between dark energy and dark matter by using optical,X-ray and weak lensing data from33relaxed galaxy clusters.In[42],Ichiki and Keum discussed the cosmological signatures of interaction between dark energy and massive neutrino(which is also a candidate for dark matter)by using CMB power spectra and matter power spectrum.Therefore,it is reasonable to consider the interaction between dark energy and dark matter in cosmology.Since dark energy can decay into cold dark matter(and vice versa)through interaction,both expansion history and growth history can be affected simultaneously,similar to the case of modified gravity.Thus,it is natural to ask whether the combined probes of expansion history and growth history can distinguish between interacting dark energy models and modified gravity models.The answer might be no.So,it is required to seek some complementary probes beyond the ones of cosmic expansion history and growth history.In this note,we propose a general approach in Sec.II to build an interacting quintessence model which shares both the same expansion history and growth history with the modified gravity model.In Sec.III, following this prescription,as an example,we explicitly demonstrate the interacting quintessence model which is indistinguishable with the DGP model in this sense.A brief discussion is given in Sec.IV,in which some suggestions to break this degeneracy are also discussed.II.GENERAL FORMALISMQuintessence[30,31]is a well-known dark energy candidate.In this section,we consider the interacting quintessence model[32,33,34,35,36,37]and show how it can share both the same expansion history and growth history with modified gravity models,without invoking non-trivial dark energy clustering.We consider aflat Friedmann-Robertson-Walker(FRW)universe.As is well known,the quintessence is described by a canonical scalarfield with a Lagrangian density Lφ=12˙φ2−V(φ),ρφ=1dφ=κQρm.(5)Using Eqs.(2)—(4),one can obtain the Raychaudhuri equation˙H=−κ22 ρm+˙φ2 .(6) It is worth noting that due to the non-vanishing interaction,ρm does not scale as a−3.The above equations are associated with the expansion history.On the side of growth history,as shown in[33],the perturbation equation in the sub-horizon regime isδ′′+ 2+H′2 1+2Q2 Ωmδ,(7)whereδ≡δρm/ρm is the linear matter density contrast;Ωm≡κ2ρm/(3H2)is the fractional energy density of cold dark matter;and a prime denotes a derivative with respect to ln a.Note that in[33]the absence of anisotropic stress has been assumed,namely,in longitudinal(conformal Newtonian)gauge the metric perturbationsΦ=Ψ.Obviously,when Q=0,Eq.(7)reduces to the standard form in general relativity[14,15,16,17,18,24,38]¨δ+2H˙δ=4πGρmδ.(8) In fact,Eq.(7)from[33]is valid for any Q=Q(φ)and generalizes the one of[34]which is only valid for constant Q.On the other hand,in modified gravity,the perturbation equation(8)has been modified to[18,21,22,38,39]¨˜δ+2˜H˙˜δ=4πGeffρm˜δ,(9)where the quantities in modified gravity are labeled by a tilde“∼”;G effis the effective local gravitational “constant”measured by Cavendish-type experiment,which is time-dependent.In general,G effcan be written asG eff=G 1+1whereβis determined once we specify the modified gravity theory.Eq.(9)can be rewrittenas˜δ′′+ 2+˜H′2 1+12δ 1+1H.(14) We can recast Eq.(3)toΩ′m=− 3+2H′H−Ω′m(κφ′)2=3+2H′Ωm 2H.(17)Noting thatδ=˜δ,we canfindδin Eq.(13)from Eq.(11).Once˜Ωm,β,˜H,and corresponding˜δin the modified gravity are given,substituting Eqs.(16)and(17)into Eq.(13)and noting Eq.(12),we obtain a differential equation forΩm with respect to ln a.After wefindΩm(ln a)from this differential equation,κφ′(ln a)can be obtained from Eq.(14),while H=˜H.Then,by using Eqs.(14)and(16), Q(ln a)=(κQφ′)/(κφ′)is in hand.From Eq.(2),Ωφ≡κ2ρφ/(3H2)=1−Ωm.Noting Eq.(1)and using Eq.(14),wefind the dimensionless potential of quintessenceU≡κ2V2+1H ,(18) where E≡H/H0.Notice that H′/H=E′/E.By integratingκφ′(ln a),wefindκφas a function of ln a. Therefore,we canfinally obtain Q,U as functions ofκφ.In fact,this general approach proposed here is just a normal reconstruction method.For any given modified gravity model,we can always construct an interacting quintessence model in the framework of general relativity which shares both the same expansion history and growth history with this given modi-fied gravity model.As is well known,an interacting quintessence model can be completely described by its potential V(φ)and the coupling Q(φ).For a given modified gravity model,its˜Ωm,β,and˜H are known, whereas its corresponding˜δcan be obtained from Eq.(11).Following the procedure described in the text below Eq.(17),one can easily reconstruct the dimensionless potential U(κφ)[which is equivalent to the potential V(φ)obviously]and the coupling Q(κφ)[which is Q(φ)in fact]for the interacting quintessence model.Up until now,the desired interacting quintessence model which shares both the same expan-sion history and growth history with the given modified gravity model has been constructed.Therefore, the cosmological observations might be unable to distinguish between them,unless other complementary probes beyond the ones of cosmic expansion history and growth history are used.6 5 4 3 2 10ln a 0.20.40.60.811.2U i n u n i t s o f 1060 0.5 1 1.5 2ln a 1020304050U 6 5 4 32 10ln a 01234ΚΦ6 5 4 3 2 10ln a 10.80.60.40.2ΚΦ' 6 5 4 3 2 10ln a 0.2 0.15 0.1 0.05Q 6 5 4 32 10ln a 0.10.20.30.40.5∆6 5 4 32 10ln a 0.20.40.60.81 m FIG.1:δ=˜δ,Ωm ,κφ′,Q ,U ≡κ2V /H 20,and κφas functions of ln a .See text for details.III.EXPLICIT EXAMPLEIn this section,we give an explicit example following the prescription proposed in Sec.II.Here,we consider the DGP braneworld model[40](see also e.g.[18,21,22,41]),which is the simplest modified gravity model.Assuming theflatness of our universe,in the DGP model(here we only consider the self-accelerating branch),˜E≡˜H/˜H0is given by[18,21,22]˜E= ˜Ωr c= ˜Ωr c,(19) where˜Ωr c is constant.˜E(z=0)=1requires˜Ωm0=1−2˜E2(z)=˜Ωm0e−3ln a1−˜Ω2m.(22) Fitting the DGP model to the192SNIa data compiled by Davis et al.[10]which are joint data from ESSENCE[9]and Gold07[3],wefind that the best-fit parameter˜Ωr c=0.170withχ2min=196.128while the corresponding˜Ωm0is given by Eq.(20).Substituting this˜Ωm0into Eqs.(21),(22)and(19),˜Ωm,β, and˜E as functions of ln a are known(since our main aim is to demonstrate the prescription proposed in Sec.II,we do not consider the errors,even one can use any˜Ωm0here for demonstration).Noting that H′/H=E′/E,following the prescription proposed in Sec.II,we can easily construct the desired interacting quintessence model which shares both the same expansion history and growth history with the corresponding DGP model.At thefirst step,we obtainδ=˜δfrom Eq.(11).As is well known,˜δ′=˜δ=a at z≫1(see e.g.[14,15]).Thus,we use the initial condition˜δ′=˜δ=a ini at z ini=1000for the differential equation(11).The resultingδ=˜δas a function of ln a is shown in Fig.1.At the second step,substituting Eqs.(16)and(17)into Eq.(13),we obtainΩm as a function of ln a from the resulting differential equation. Note that cold dark matter can decay to quintessence through interaction,Ωm is unnecessary to be1at high redshift.So,for demonstration,we choose the initial conditionΩm(z=z ini)=0.995at z ini=1000 for the differential equation ofΩm.Different values ofΩm(z=z ini)only mean different displacements of κφ′and the dimensionless potential U≡κ2V/H20at z ini.The resultingΩm as a function of ln a is also shown in Fig.1.Then,following the prescription proposed in Sec.II,it is straightforward to obtainκφ′, Q,U≡κ2V/H20,andκφas functions of ln a,while for demonstration we choose the negative branch for κφ′,and chooseφ0=0when we getκφ.They are also shown in Fig.1.Once we obtain Q,U andκφas functions of ln a,it is easy tofind Q and U as functions ofκφ.The results are shown in Fig.2.In short,here we have faithfully followed the reconstruction method proposed in Sec.II,and successfully constructed an interacting quintessence model which shares both the same expansion history and growth history with the DGP model whose single model parameter˜Ωr c=0.170which is the best-fit to the 192SNIa data compiled by Davis et al.[10]for example.The potential V(φ)and coupling Q(φ)which are required to describe the reconstructed interacting quintessence model have been presented in Fig.2 through the equivalent U(κφ)and Q(κφ).There are no analytical expressions for them and instead the reconstructed U(κφ),Q(κφ)are given in numerical forms.IV.CONCLUSION AND DISCUSSIONIn summary,we proposed a general approach to build an interacting quintessence model which shares both the same expansion history and growth history with the modified gravity model.Therefore,thecosmological observations might be unable to distinguish between them,unless other complementary probes beyond the ones of cosmic expansion history and growth history are used.As an example,we also explicitly demonstrated the interacting quintessence model which is indistinguishable with the DGP model in this sense.In fact,this proposed prescription is also valid for other modified gravity models,such as f (R )theories,braneworld-type models,scalar-tensor theories (including Brans-Dicke theory),TeVeS/MOND models,and so on [43,44,45].Of course,one can also extend the interacting quintessence model to other interacting dark energy models.0.51 1.522.533.5ΚΦ 0.20.150.1 0.050Q 0.51 1.52 2.53 3.5ΚΦ0.20.40.60.811.2U i n u n i t s o f 1060.51 1.52ΚΦ10203040U FIG.2:Q and U ≡κ2V /H 20as functions of κφ.In this note,without invoking non-trivial dark energy clustering (e.g.non-vanishing anisotropic stress),we find that the interaction between dark energy and dark matter could also make dark energy model and modified gravity model indistinguishable.How can we break this degeneracy?Firstly,we should carefully check the evidences of the interaction between dark energy and dark matter [28,29,42].If this interaction does not exist,the combined probes of cosmic expansion history and growth history might be enough to distinguish between dark energy and modified gravity.It is worth noting that the current observational constraints on the interaction between dark energy and dark matter in the literature (e.g.[28,29,42,46])considered other interaction forms (e.g.∝Hρm ,Hρde or Hρtot )which are different from the one of the present work [cf.Eqs.(3)and (4)],and hence cannot be used to compare with the interaction considered here.Therefore,it is of interest to consider the observational constraints on the type of interactions ∝Q (φ)ρm ˙φin future works.Secondly,to break the degeneracy,the other complementary probes beyond the ones of cosmic expansion history and growth history are desirable.For instance,these complementary probes might include local tests of gravity,high energy phenomenology,and non-linear structure formation.Thirdly,in addition to the linear matter density contrast δ(z ),one can also test the metric perturbations Φand Ψby using the relationship between gravitational lensing and matter overdensity [50].For the interacting quintessence model Φ=Ψ,whereas for the DGP model Φ=Ψ.Thus,it is possible to distinguish between them by using delicate measurements.We consider that this issue deserves further investigations and believe that a promising future is awaiting us.ACKNOWLEDGMENTSWe thank the anonymous referee for comments,which helped us to improve this manuscript.We are grateful to Prof.Rong-Gen Cai,Prof.Pengjie Zhang,Prof.Bin Wang and Prof.Xinmin Zhang for helpfuldiscussions and comments.We also thank Minzi Feng,as well as Nan Liang,Rong-Jia Yang,Wei-Ke Xiao, Pu-Xun Wu,Jian Wang,Lin Lin,Bin Fan and Yuan Liu,for kind help and discussions.The major part of this work was completed during March16–23,2008.We acknowledge partial funding support from China Postdoctoral Science Foundation,and by the Ministry of Education of China,Directional Research Project of the Chinese Academy of Sciences under Project No.KJCX2-YW-T03,and by the National Natural Science Foundation of China under Project 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The physics of dark energy and itsapplicationsDark energy is a mysterious force that pervades the entire universe. Its presence has been confirmed through various astronomical observations and cosmological studies, yet its nature and origin remain unknown. In this article, we will explore the physics of dark energy and some of its potential applications in astrophysics and beyond.What is Dark Energy?Dark energy is a hypothetical form of energy that permeates all of space and acts as a repulsive force, causing the expansion of the universe to accelerate. The concept of dark energy was first proposed in the late 1990s, after astronomers discovered that distant galaxies were receding from us at a faster rate than expected. This suggested that the universe was expanding at an accelerating rate, which could not be explained by the known laws of physics.One possible explanation for this phenomenon is the existence of a cosmological constant, which is a term in Einstein's theory of general relativity that represents a repulsive force. However, the value of the cosmological constant required to explain the observed acceleration is much smaller than what would be predicted by quantum field theory, leading to the cosmological constant problem.Another possible explanation is that dark energy is a dynamical field that varies with time and space, known as quintessence. This theory proposes that the acceleration of the universe is driven by the potential energy of a scalar field that permeates all of space.Despite numerous efforts to detect and study dark energy, its nature remains elusive. It is believed to account for about 70% of the total energy content of the universe, making it the dominant component of the universe's energy budget.How is Dark Energy Studied?Dark energy cannot be directly observed or measured in a laboratory, as it interacts very weakly with matter and radiation. Instead, scientists rely on its effects on the expansion of the universe and the large-scale structure of galaxies and galaxy clusters.One of the most important observational probes of dark energy is the cosmic microwave background (CMB) radiation, which is the residual heat left over from the Big Bang. Variations in the CMB provide clues about the geometry and evolution of the universe, as well as the distribution of matter and dark energy.Another powerful tool for studying dark energy is the observation of Type Ia supernovae, which are exploding stars that have a known brightness and can be used as standard candles to measure distances in the universe. By observing how the brightness of these supernovae changes over time, astronomers can infer the expansion rate of the universe and the presence of dark energy.Other methods for studying dark energy include weak gravitational lensing, which measures the distortion of light from distant galaxies as it passes through the intervening matter, and baryon acoustic oscillations, which are periodic ripples in the density of matter that provide a standard ruler for cosmological distances.Applications of Dark EnergyAlthough the nature of dark energy remains enigmatic, its potential applications in astrophysics and beyond have been explored by scientists and engineers.One of the most promising applications of dark energy is in the design of advanced propulsion systems for space exploration. Because dark energy is a repulsive force that acts over long distances, it could be harnessed to propel spacecraft to velocities approaching the speed of light. However, this requires understanding the nature of dark energy more deeply and developing technology that can manipulate it.Another possible application of dark energy is in the development of new materials and energy sources. Some researchers have proposed using the unique properties of dark energy to create exotic materials that could be used in electronics, optics, and other fields.Finally, dark energy could have implications for our understanding of the fundamental physics of the universe. Some theories propose that dark energy is related to the properties of fundamental particles and forces, and that a deeper understanding of dark energy could lead to a unified theory of physics.ConclusionThe physics of dark energy remains one of the most intriguing and challenging topics in modern cosmology. Its presence has been confirmed by numerous observational probes, but its true nature and origin remain elusive. Nevertheless, the potential applications of dark energy in space exploration, materials science, and fundamental physics make it an area of active research and speculation. As we continue to explore the mysteries of the universe, dark energy will undoubtedly play a central role in our quest for understanding.。

a r X i v :g r -q c /0210079v 1 23 O c t 2002DARK ENERGY,DARK MATTER ANDTHE CHAPLYGIN GASR.Colistete Jr.1,J.C.Fabris 2,S.V.B.Gon¸c alves 3and P.E.de Souza 4Departamento de F´ısica,Universidade Federal do Esp´ırito Santo,CEP29060-900,Vit´o ria,Esp´ırito Santo,BrazilAbstract The possibility that the dark energy may be described by the Chaplygin gas is discussed.Some observational constraints are established.These observational constraints indicate that a unified model for dark energy and dark matter through the employement of the Chaplygin gas is favored.PACS number(s):98.80.Bp,98.65.Dx The possible existence of dark matter and dark energy in the Universe constitutes one of the most important problems in physics today.One calls dark matter the mysteri-ous component of galaxies and clusters of galaxies that manifestates itself only through gravitational effects,affecting only the dynamics of those object.Dark matter appears in collapsed objects.The existence of dark energy,on the other hand,has been speculated due to the observation of the Universe as a whole.In particular,the position of the first accoustic peak in the spectrum of the anisotropy of the cosmic microwave background radiation[1]and the data from supernova type Ia[2,3]suggest that the dynamics of the Universe is such that the most important matter component is non-clustered,exhibit-ing negative pressure.The current observations favor Ωdm ∼0.3and Ωde ∼0.7for the proportion of dark matter and dark energy.The most natural candidate to represent dark energy is a cosmological constant[4].However,it is necessary a fine tunning of 120orders of magnitude in order to obtainagreement with observations.Another popular candidate today is quintessence,a self-interacting scalar field[5,6,7].But the quintessence program suffers from fine tuning of microphysical paremeters.In this work,we discuss the possibility that the dark energy may be represented by the Chaplygin gas[8,9,10,11,12],which is characterized by the equation of state p =−A 1e-mail:coliste@ccr.jussieu.fr 2e-mail:fabris@cce.ufes.br 3e-mail:sergio@cce.ufes.br 4e-mail:patricia.ilus@.brcharacter of the action is somehow hidden in the equation of state (1).For a review of the properties of the Chaplygin gas see reference [13].Using the relativistic equation of conservation for a fluid in a FRW background,we obtain that the density of the Chaplygin gas depends on the scale factor asρ= a 6.(2)Hence,initially the Chaplygin gas behaves as a pressurelless fluid and assumes asymp-totically a behaviour typical of a cosmological constant.In this sense,the Chaplygin gas may be an alternative for the description of dark energy.Remark that,even if the pressure associated with the Chaplygin gas is negative,the sound velocity is real.Hence,no instability problem occurs as it happens with other fluids with negative pressure[14].In reference [9]the density perturbations in a Universe dominated by the Chaplygin gas was investigate.In that work,the fact that the Chaplygin gas may be represented by a newtonian fluid was explored.The density contrast behaves asδ=t −1/6 C 1J ν(Σ2nt 7/3)+C 2J −ν(Σ2nt 7/3) ,(3)where n is the wavenumber of the perturbations,ν=5/14and Σ2=54a 20,a 0is a constant and C 1and C 2are constants that depend on n .A simple analysis of this solutionindicates that initially the perturbations behave as in the case of the pressurelless fluid,presenting asymptotically oscillatory behaviour with decreasing amplitude,approaching a zero value typical of a cosmological constant.Even if this result was obtained in a newtonian context,a numerical analysis of the corresponding relativistic equations exhibit the same behaviour.In reference [10],the mass power spectrum of the perturbations in a Universe domi-nated by the Chaplygin gas was computed.The matter content was assumed to be com-posed of radiation,dark matter and dark energy,the latter represented by the Chaplygin gas.Due to the complexity of perturbed equations,a numerical analysis was performed.The initial spectrum,at the moment of decoupling of radiation and matter,was supposed to be the Harrisson-Zeldovich scale invariant spectrum.Taken at constant time,this implies to impose an initial spectral index n s =5.The system evolves and the power spectrum is computed for the present time.The final results were obtained for a Universe dominated uniquely by a pressurelless fluid (baryonic model ),for a cosmological constant model and for a mixed of dark matter and Chaplygin gas,with different values for thesound velocity of the Chaplygin gas,defined as v 2s =¯A =A/ρ2c 0,where ρc 0is the Chaply-gin gas density today.When ¯A =1the Chaplygin gas becomes identical to a cosmologicalconstant.It was verified that the Chaplygin gas models interpolate the baryonic model and the cosmological constant model as ¯Avaries from zero to unity.The results for the power spectrum P (n )=n 3/2δn in terms of n/n 0,where n 0is reference scale correspond-ing to 100Mpc ,are displayed in figure 1for the baryonic model,cosmological constant model and for the Chaplygin gas model with different values for ¯A.The spectral indice for perturbations of some hundreds of megaparsecs up to the Hubble radius is n s ∼4.7for the baryonic model,n s∼4.2for the cosmological constant model,n s∼4.5for the Chaplygin gas with¯A=0.5.Another important test to verify if the Chaplygin gas model may represent dark energy is the comparison with the supernova type Ia data.In order to do so,we evaluate the luminosity distance[15]in the Chaplygin gas cosmological model.In such a model,the luminosity distance,for aflat Universe,readsD L=(1+z) z0dz′Ωm0(1+z′)3+Ωc0¯A+(1−¯A)(1+z′)6 .(5) In order to compare with the supernova data,we compute the quantityµ0=5log D Lσ2µ0,i +σ2mz,i.(7)In this expression,µo0,i is the measured value,µt0,i is the value calculated through themodel described above,σ2µ0,i is the measuremente error,σ2mz,i is the dispersion in thedistance modulus due to the dispersion in galaxy redshift due to perculiar velocities.This quantity we will taken asσmz=∂log D Lmay unify dark matter with dark energy:at small scales,the Chaplygin gas may cluster, playing the role of dark matter,remaining a smooth component at large scale[8,11,12].The results presented above indicate that the Chaplygin gas may be taken seriously as a candidate to describe dark energy and dark matter.However,more analysis are needed in order to verify to which extent it can be a better alternative with respect to the cosmological constant model combined with dark energy.A crucial test is the analysis of the spectrum of anisotropy of the cosmic microwave background radiation. References[1]C.H.Lineweaver,Cosmological parameters,astro-ph/0112381;[2]A.G.Riess et al,Astron.J.bf116,1009(1998);[3]S.Permultter et al,Astrophys.J.517,565(1998);[4]S.M.Carroll,Liv.Rev.Rel.4,1(2001);[5]R.R.Caldwell,R.Dave and P.Steinhardt,Phys.Rev.Lett.80,1582(1998);[6]V.Sahni,The cosmological constant problem and quintessence,astro-ph/0202076;[7]Ph.Brax and J.Martin,Phys.Lett.B468,40(1999);[8]A.Kamenshchik,U.Moschella and V.Pasquier,Phys.Lett.B511,265(2001);[9]J.C.Fabris,S.V.B.Gon¸c alves and P.E.de Souza,Gen.Rel.Grav.34,53(2002);[10]J.C.Fabris,S.V.B.Gon¸c alves e P.E.de Souza,Mass power spectrum in a Universedominated by the Chaplygin gas,astro-ph/0203441;[11]N.Bilic,G.B.Tupper and R.D.Viollier,Phys.Lett.B535,17(2002);[12]M.C.Bento,O.Bertolami and A.A.Sen,Generalized Chaplygin gas,acceleratedexpansion and dark energy-matter unification,gr-qc/0202064;[13]R.Jackiw,A particlefield theorist’s lectures on supersymmetric,non-abelianfluidmechanics and d-branes,physics/0010042;[14]J.C.Fabris and J.Martin,Phys.Rev.D55,5205(1997);[15]P.Coles and F.Lucchin,Cosmology,Wiley,New York(1995).0.20.40.60.81n/n0200400600800P(n)Figure 1:The power spectrum P (n )=n 3/2δn as function of n/n 0.Log cz343638404244m -MFigure 2:The the best fitting model,where Ωm 0=0,Ωc 0=1,¯A∼0.847and H 0∼62.1.。

探索宇宙奥秘英文作文The universe is a vast and mysterious place, full of endless wonders and secrets waiting to be discovered. From the twinkling stars in the night sky to the swirling galaxies millions of light years away, there is so much we still don't know about the cosmos.As we gaze up at the night sky, it's easy to feel small and insignificant in the grand scheme of the universe. Yet, at the same time, it's awe-inspiring to think about how much there is out there still waiting to be explored and understood.Scientists and astronomers have dedicated their lives to unraveling the mysteries of the universe, using advanced technology and telescopes to peer deeper into space than ever before. With each new discovery, we come closer to understanding the origins of the universe and our place within it.One of the most intriguing questions about the universe is whether we are alone. Are there other intelligent beings out there, living on distant planets or in far-off galaxies? The search for extraterrestrial life continues to captivate our imaginations and drive our exploration of the cosmos.The concept of dark matter and dark energy adds another layer of mystery to the universe. These invisible forces make up the majority of the universe's mass and energy, yet we still know so little about them. Unraveling the secretsof dark matter and dark energy could hold the key to understanding the fate of the universe itself.The study of black holes also presents a fascinatingand enigmatic aspect of the universe. These cosmic phenomena are so dense and powerful that not even light can escape their grasp. They challenge our understanding of physics and the very nature of space and time.In the end, the universe remains a vast and enigmatic frontier, filled with countless mysteries waiting to be uncovered. Our ongoing exploration of the cosmos continuesto push the boundaries of human knowledge and inspire us to dream of what lies beyond the stars.。

A Many Worlds Interpretation of the Dark Universe Richard Douglas Bateson【期刊名称】《Journal of High Energy Physics, Gravitation and Cosmology》【年(卷),期】2024(10)2【摘要】In this paper, we discuss a Many Worlds Interpretation (MWI) of Dark Energy and Dark Matter. The universe is viewed cosmologically as a fermionic fluid with a hydrostatic pressure from “Zitterbewegung”, the quantum “zig-zagging” of Dirac particles. At each point in space-time, the pressure from all possible velocity states existing in the Many Worlds sums to provide a dark energy. This provides a ratio of matter energy to pressure energy close to that observed experimentally. Visible matter isthe matter observed or measured in a particular velocity state and dark matter is then considered as the unobserved fermion contributions from different orthogonal spatial directions.【总页数】8页(P828-835)【作者】Richard Douglas Bateson【作者单位】Cavendish Laboratory, Cambridge, UK【正文语种】中文【中图分类】O41【相关文献】1.Proof of Hubble’s Law and the Truth about the Expansion of the Universe as Well as Dark Matter and Dark Energy2.A Unifying Theory of Dark Energy, Dark Matter, and Baryonic Matter in the Positive-Negative Mass Universe Pair: Protogalaxy and Galaxy Evolutions3.Explanation ofDark Matter, Dark Energy and Dark Space: Discovery of Invisible Universes4.If Quantum “Wave” of the Universe Then Quantum “Particle” of the Universe: A Resolution of the Dark Energy Question and the Black Hole Information Paradox5.Towards a unified interpretation of the early Universe in R^(2)-corrected dark energy model of F(R)gravity因版权原因，仅展示原文概要，查看原文内容请购买。

a r X i v :h e p -p h /0503120v 1 14 M a r 2005Possible Effects of Dark Energy on the Detection of Dark MatterParticlesPeihong Gu,1Xiao-Jun Bi,2Zhi-Hai Lin,1and Xinmin Zhang 11Institute of High Energy Physics,Chinese Academy of Sciences,P.O.Box 918-4,Beijing 100049,P.R.China2Key laboratory of particle astrophysics,Institute of High Energy Physics,Chinese Academy of Sciences,P.O.Box 918-3,Beijing 100049,P.R.China (Dated:February 2,2008)Abstract We study in this paper the possible influence of the dark energy on the detection of the dark matter particles.In models of dark energy described by a dynamical scalar field such as the Quintessence,its interaction with the dark matter will cause the dark matter particles such as the neutralino vary as a function of space and time.Given a specific model of the Quintessence and its interaction in this paper we calculate numerically the corrections to the neutralino masses and the induced spectrum of the neutrinos from the annihilation of the neutralinos pairs in the core of the Sun.This study gives rise to a possibility of probing for dark energy in the experiments of detecting the dark matter particles.Recent observational data from supernovae(SN)Ia[1]and cosmic microwave background radiation(CMBR)[2]strongly support for the‘cosmic concordance’model,in which the Universe is spatiallyflat with4%baryon matter,23%of cold dark matter(DM)and 73%of dark energy(DE).The baryon matter is well described by the standard model of the particle physics,however the nature of the dark matter and the dark energy remains unknown.There have been many proposals in the literature for the dark matter candidates the-oretically.From the point of view of the particle physics,the leading candidates for cold dark matter are the axion and the neutralino.Various experiments in the search directly or indirectly for these dark matter particles are currently under way.Regarding dark energy,the simplest candidate seems to be a remnant small cosmological constant.However,many physicists are attracted by the idea that dark energy is due to a dynamical component,such as a canonical scalarfield Q,named Quintessence[3].Being a dynamical component,the scalarfield of the dark energy is expected to interact with the other matters[4].There are many discussions on the explicit couplings of quintessence to baryons,dark matter,photons and neutrinos.These interactions if exist will open up the possibilities of probing non-gravitationally for the dark energy.In this paper we consider the possible effects of the dark energy models which interact with the dark matter in the detection of the dark matter particles.Specifically we will study the influence of the dark energy on the neutralino masses in the Sun,and then calculate the neutrino spectrum annihilated from the neutralino pairs in the core of the Sun.We start with a coupled system of the interacting dark energy and the dark matter with the Lagrangian generally given byL eff=L DM+Lφ+L int,(1)where L DM and Lφare the free Lagrangian for dark matter and dark energy and the inter-action part is given byL int=−12M2S(φ)S2−gχΛ∂µφ¯ψγµψ−g SΛφ∂µφ∂µS− g isuch as the neutralino to be the dark matter particle and focus on the interactions which affect the dark matter particles via the mass terms.Being a function of the quintessence scalarφthe mass of the dark matter particle will vary during the evolution of the universe.As shown in Refs.[5,6,7]this helps solve the coincidence problem.Furthermore,this type of interactions will affect the cosmic structure formation[8],and the power spectrum of CMB[9].In this paper we will present a new possible effect of the interacting dark energy with the dark matter in the detection of the dark matter particles.There are in general two different ways,direct and indirect,in the detections of the dark matter particles.The direct detection records the recoil energy of the detector nuclei when the dark matter particles scatter offthem as they pass through the Earth and interact with the matter.The indirect detection observes the annihilation products by the dark matter particles.Obviously the expected detection rates depend on the mass of the dark matter particles.In the presence of the interaction the mass of the dark matter particle will vary as a function of time and also space,and consequently the dark energy will influence the detection.To determine the mass of neutralino as a function of space we need to know the value of the dark energy scalarfield as a function of space.Taking into account the back reaction of the interaction between the dark matter and the dark energy the effective potential of the dark energy scalar as a function of the energy density of the cold dark matterρχ(φ)is given byV eff=ρχ(φ)+V(φ).(3) For different dark matter densities the values of dark energy scalarfield are expected to be different,and consequently the mass of dark matter particles will also be different.For example,the mass of the dark matter particle in the center of the Milky Way could be different from that in the halo near the solar system.Therefore,the gamma ray spectrum, or the synchrotron radiation spectrum,from the galactic center could be different from that in the nearby halo.Especially for the neutralino dark matter particle its mass measured at the future linear collider(LC)or the large hadron collider(LHC)on the Earth may be different from that measured in other places in the Milky Way,such as in the galactic center.Similarly,the spectrum of the dark matter radiation in the Milky Way might also be different from other galaxies in the local group.In the following we will consider a specific model of the Quintessence and its interaction with the dark matter particle,the neutralino,and then study its effects on the indirect detection via the process of the neutralinos annihilation into neutrinos.The dark energy potential which we take isV(φ)=V0eβφ/m p,(4) and the interaction between the dark energy and the dark matter particle are given byMχ(φ)=Mχ0 1+λχφ(y q¯Q L Hq R).(6)m pThe parameterλB above characterizing the strength of this type of interaction will be shown below to be strongly constrained.However,since the baryon density inside the Sun is much higher than any other matter densities,this interaction in Eq.(6)will be important to our study in this paper as well as that on the neutrino oscillations[14,17,18].The Eq.(5)shows that the mass of the dark matter particles varies during the evolution of the Universe.At the present time the mass of the neutralino dark matter particle is given by Eq.(5)with the scalarfieldφevaluated at the present timeφ0.This type of physics associated with the mass varying dark matter particles have been proposed and studied in the literature[6,9,19],but in these studies the masses of the dark matter particle are constant in space.In this paper we consider the case that neutralino masses vary as afunction of space,for instance the neutralino mass in the Sun differs from that evaluated on the cosmological scale.The effective potential of the dark energy scalar at the inner of the Sun or the Earth is given byV eff =ρB (φ)+ρχ(φ)+V (φ),(7)where ρB (φ)is the mass density of the baryon matter and ρχ(φ)=n χM χ(φ).Here it’s straightforward to obtain ρB (φ)=ρB 0−λB ρB 0φdφφ=φmin=0.(8)The contributions to the equation above from the dark matter and baryon are proportional to λB ρB and λχρχrespectively.Sincethe ρχis about 15orders of magnitude smaller than ρB in the core of the Sun [20],the influence of the dark matter on the effective potential of the dark energy scalar can be safely ignored ifλB ≫λχρχβln λB ρBM cos χ=1+λχβV 0m p .(11)In Eq.(11)φ0is the cosmological value of the scalar field at the present time.To satisfy the cosmological observations on the dark energy our numerical results show that φ0=−0.51m p ,V 0=4.2×10−47GeV 4and β=1and λχ=0.1which we have mentioned above.10-510-410-310-210-1100200300400500600700800900E µ(GeV)ΦµM χ=170GeV M χ=1TeVFIG.1:Spectra of the muons induced by the neutrinos from the annihilation of the neutralino dark matter particles in the core of the Sun with m χ=1TeV and in the cosmological scale with m χ=170GeV.The spectra are normalized at 10GeV and calculated by using the DarkSUSY package [23].The baryon energy density of the Sun ρ⊙B is about 2.5g/cm 3.However due to thelogarithm in Eq.(10),the effect on the dark matter mass is insensitive to the baryon mass density ρB .For example,the baryon density in the Sun ρ⊙B is about a quarter of that inthe Earth,which causes that M ⊙χis about 2%smaller than the value at the Earth in ournumerical calculation for λB =10−9.The parameter λB is constrained by the tests on the gravitational inverse square law [21]and the tests on the equivalence principle [22]to be λB <∼O (10−2).Here we point out that the presence of the interaction of the dark energy with the baryon in Eq.(6)makes the baryon mass density also varyδρBρB =−λB βV 0.(12)If taking ρB (φmin )to be the baryon density in the Earth (which is similar to the baryon density of the Sun),δρB (φmin )indicates the correction of the dark energy to baryon mass in the Earth.The proton mass has been measured very precisely on the Earth with an error of 10−8.If we take as an example that δρB /ρB <10−8we obtain an upper limit on λB ,λB <10−9,which we use in the numerical calculation.Now we have φmin ≃49m p and consequently M ⊙χ/M cos χ≃6.In Fig.1we plot the muonspectra induced by the neutrino from the dark matter annihilation in the center of the Sun and in the cosmological scale.We choose the dark matter mass in the Sun to be1TeV, while the dark matter mass in the cosmological scale is about1TeV/6=170GeV.From the figure one can see clearly the difference in the neutrino spectra.On the cosmological scale the dark energy scalar is homogeneously distributed,however in this case it is inhomogeneous,which gives rise to energy densityρφin the Sun.From Eqs.(4)and(10)we haveρφρB =λB[4]See,for 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a r X i v :a s t r o -p h /0507459v 1 19 J u l 2005Supernova Acceleration Probe:Studying Dark Energy withType Ia SupernovaeA White Paper to the Dark Energy Task ForceJ.Albert 1,G.Aldering 2,S.Allam 3,W.Althouse 4,R.Amanullah 5,J.Annis 3,P.Astier 6,M.Aumeunier 7,8,S.Bailey 2,C.Baltay 9,E.Barrelet 6,S.Basa 8,C.Bebek 2,L.Bergstr¨o m 5,G.Bernstein 10,M.Bester 11,B.Besuner 11,B.Bigelow 12,R.Blandford 4,R.Bohlin 12,A.Bonissent 7,C.Bower 13,M.Brown 12,M.Campbell 12,W.Carithers 2,D.Cole 14,mins 2,W.Craig 4,T.Davis 15,2,K.Dawson 2,C.Day 2,M.DeHarveng 8,F.DeJongh 3,S.Deustua 16,H.Diehl 3,T.Dobson 11,S.Dodelson 3,A.Ealet 7,8,R.Ellis 1,W.Emmet 9,D.Figer 12,D.Fouchez 7,M.Frerking 14,J.Frieman 3,A.Fruchter 12,D.Gerdes 12,L.Gladney 10,G.Goldhaber 11,A.Goobar 5,D.Groom 2,H.Heetderks 11,M.Hoff2,S.Holland 2,M.Huffer 4,L.Hui 3,D.Huterer 17,B.Jain 10,P.Jelinsky 11,C.Juramy 6,A.Karcher 2,S.Kent 3,S.Kahn 4,A.Kim 2,W.Kolbe 2,B.Krieger 2,G.Kushner 2,N.Kuznetsova 2,fever 2,moureux 2,mpton 11,O.Le F`e vre 8,V.Lebrun 8,M.Levi 2∗,P.Limon 3,H.Lin 3,E.Linder 2,S.Loken 2,W.Lorenzon 12,R.Malina 8,L.Marian 10,J.Marriner 3,P.Marshall 4,R.Massey 18,A.Mazure 8,B.McGinnis 2,T.McKay 12,S.McKee 12,R.Miquel 2,B.Mobasher 12,N.Morgan 9,E.M¨o rtsell 5,N.Mostek 13,S.Mufson 13,J.Musser 13,R.Nakajima 10,P.Nugent 2,H.Olus .eyi 2,R.Pain 6,N.Palaio 2,D.Pankow 11,J.Peoples 3,S.Perlmutter 2†,D.Peterson 2,E.Prieto 8,D.Rabinowitz 9,A.Refregier 19,J.Rhodes 1,14,N.Roe 2,D.Rusin 10,V.Scarpine 3,M.Schubnell 12,M.Seiffert 14,M.Sholl 11,H.Shukla 11,G.Smadja 20,R.M.Smith 1,G.Smoot 11,J.Snyder 9,A.Spadafora 2,F.Stabenau 10,A.Stebbins 3,C.Stoughton 3,A.Szymkowiak 9,G.Tarl´e 12,K.Taylor 1,A.Tilquin 7,A.Tomasch 12,D.Tucker 3,D.Vincent 6,H.von der Lippe 2,J-P.Walder 2,G.Wang 2,A.Weinstein 1,W.Wester 3,M.White 11saul@ melevi@16AmericanAstronomical Society 17Universityof Chicago18Cambridge University 19CEA,Saclay,France20IPNL,CNRS-IN2P3,Villeurbanne,France ∗Co-PI †PInova distance measurements up to their funda-mental systematic limit;strict requirements on the monitoring of each supernova’s properties leads to the need for a space-based mission.Results from pre-SNAP experiments,which characterize fundamental SN Ia properties,will be used to op-timize the SNAP observing strategy to yield data, which minimize both systematic and statistical uncertainties.With early R&D funding,we have achieved technological readiness and the collabo-ration is poised to begin construction.Pre-JDEM AO R&D support will further reduce technical and cost risk.Specific details on the SNAP mission can be found in Aldering et al.(2004,2005).1.1.Overview of Goals and TechniquesThe primary goal of the SNAP supernova pro-gram is to provide a dataset which gives tight constraints on parameters which characterize the dark-energy,e.g.w0and w a where w(a)=w0+ w a(1−a).SNAP data can also be used to di-rectly test and discriminate among specific dark-energy models.We will do so by building the Hub-ble diagram of high-redshift supernovae,the same methodology used in the original discovery of the acceleration of the expansion of the Universe that established the existence of dark energy(Perlmut-ter et al.1998;Garnavich et al.1998;Riess et al. 1998;Perlmutter et al.1999).The SNAP SN Ia program focuses on minimiz-ing the systematicfloor of the supernova method through the use of characterized supernovae that can be sorted into subsets based on subtle signa-tures of heterogeneity.Subsets may be defined based on host-galaxy morphology,spectral-feature strength and velocity,early-time behavior,inter alia.Independent cosmological analysis of each subset of“like”supernovae can be compared to give confidence that the results are free from sig-nificant systematics.Conversely,analysis between supernova subsets at the same redshift can iden-tify further systematics controls.While theories of the supernova progenitor and explosion mech-anism can guide the establishment of subset cri-teria,such understanding is not required–only comprehensive measurements are–for robustness of the cosmological results.The level of robustness is tied to the quality of data with which supernovae are distinguished.Statistical mission requirements are fundamentally bound by the systematic limi-tations of the experiment.1.2.Description of the Baseline ProposalSNAP is a2-m space telescope(shown in Fig-ure1)with a0.7square-degree instrumented focal plane imager(shown in Figure2)and a low res-olution R∼100integral-field-unit spectrograph (schematic shown in Figure3).Both instruments are sensitive to the0.4–1.7µm wavelength range. The two SNAP deep-surveyfields each subtends 7.5square degrees and each is observed approx-imately every four days over the time-scales of supernova light-curve evolution in each of nine passbands.The passbands have resolution∼4.5 and are logarithmically distributed over the full wavelength range.Targeted spectrographic obser-vations are made of discovered supernovae with exposure times tuned to the sourceflux.The magnitude depths for individual scans and co-added images of the SNAP supernovafields are calculated for eachfilter.Table1shows the limit-ing S/N=5AB magnitude for eachfilter in the “Deep”supernova survey,for point sources that are not contaminated with cosmic rays.The limit-ing magnitude for any given point is probabilistic, due to the random occurrence of cosmic rays.In a single scan of the deep survey,77%of point sources will have no cosmic-ray contamination in any of the four dithered images while98%will have one or fewer cosmic-contaminated image,only slightly reducing signal-to-noise.2.Precursor ObservationsAny precursor mission that characterizes the fundamental properties of SNe Ia and their ap-plicability as distance indicators is important for optimizing the observing strategy and data anal-ysis of SNAP.Low-redshift surveys provide high signal-to-noise,comprehensive observations of well-charac-terized SNe Ia and could provide specific require-ments for the observation of light-curve or spec-troscopic features linked to SN Ia heterogeneity and homogeneity.Heterogeneous features provide a handle to probe the systematic limitations of our distance indicator and form the criteria by which “like”supernova subsets are defined.Conversely, current distance measurements to supernovae may be found not to be optimal;a different mix of ob-Table1The SNAP AB magnitude survey depth for a point source S/N=5.a Filterλeff(˚A)∆λ(˚A)Deep Survey(AB mag)Wide-field Survey Panoramic 14400100027.930.628.326.7 25060115027.930.628.326.8 35819132227.830.528.226.8 46691152027.830.428.126.8 57695174927.830.428.126.8 68849201127.730.328.026.7 710177231327.530.127.826.6 811704266027.530.127.826.6 913459305927.430.027.726.51.5 degreeFig.2.—The SNAP focal plane working concept. The two-axis symmetry of the imagerfilters allows any90◦rotation to scan afixed strip of the sky and measure all objects in all ninefilter types.The im-ager covers0.7square degrees.Underlying thefil-ters,there are362k x2k HgCdTe NIR devices and 363.5k x3.5k CCDs on a140K passively-cooled focal plane.The six CCDfilter types and three NIRfilters are arranged so that vertical or hori-zontal scans of the array through an observation field will measure all objects in allfilters.The false colors indicatefilters with the same bandpass.The central rectangle and solid circle are the spectro-graph body and its light access port,respectively. The spectrum of a supernova is taken by placing the star in the spectrograph port by steering the satellite.The four small,isolated squares are the star guider CCDs.The inner and outer radii are 129and284mm,respectively.Fig. 3.—A schematic spectrograph optical de-sign.The beam is going out from the slicer(on the bottom right)to a prism disperser back faced coated by a dichroic.The visible light(blue path) is reflected and the IR light(in red)continue to a second prism used to reach the required spectral dispersion.The two beams are therefore focused on two detectors.The dimensions of the spectro-graph are approximately400×80×100mm.See Ealet et al.(2003)for more details.dark-energy properties,especially the time vari-ation of the equation of state.3.1.Sources of Systematic UncertaintyHigh-redshift supernova searches have been proceeding since the late1980’s(Norgaard-Nielsen et al.1989;Couch et al.1989;Perlmutter et al. 1995,1997,1998,1999;Schmidt et al.1998;Riess et al.1998;Tonry et al.2003;Knop et al.2003; Riess et al.2004).Particularly since the discov-ery of the accelerating expansion of the Universe, the high-redshift supernova methodology for mea-suring cosmological parameters has been critically scrutinized for sources of systematic uncertainty. Below(and summarized in Table2)is a lists of these sources where we highlight in bold the fea-tures specific to SNAP that allow systematic con-trol.Generically,the need for high signal-to-noise observations over a broad wavelength range for 0.1<z<1.7supernovae,as well as the truncation of ground-observatory light curves of high-redshift supernova at high-Galactic latitude,point to the necessity of a space mission.Table2SNAP Control of Sources of Astrophysical Systematic Uncertainty Systematic Control3.1.1.Evolution of the Supernova Sample as aFunction of RedshiftThe luminosity function of supernovae may evolve as a function of redshift resulting in cor-responding biases in distance-modulus determina-tions(Perlmutter et al.1995).Although like su-pernovae have the same redshift-independent lu-minosity,their relative rate of occurrence may evolve in redshift.SNAP addresses this problem by identifying subsets of supernovae“identical”in luminosity and color,applying the dark-energy analysis to each,and optimally combining the subset re-sults intofinal cosmology measurements.We exploit the fact that supernovae cannot change their brightness in one measured wavelength range without affecting brightness somewhere else in the spectral time series—an effect that is well-captured by expanding atmosphere computer models(e.g.H¨oflich&Khokhlov1996;Lentz et al. 2000;H¨oflich et al.2003).Well-characterized su-pernovae can be sorted into subsets based on sub-tle signatures of heterogeneity.Subsets may be de-fined based on host-galaxy morphology,spectral-feature strength and velocity,early-time behavior, and light-curve characteristics.There are a number of supernova parameters that are observed to exhibit heterogeneity beyond the single-parameter description.The following features need to be monitored to check for sys-tematic bias in supernova distances.Premaximum spectral screening:Broad-light-curve supernovae can be distinguished by hav-ing either peculiar(e.g.SN1991T)or“normal”(e.g.SNe1999ee and2000E)pre-maximum spec-tra.In addition,there are extremely peculiar sin-gleton events technically classified as SNe Ia which bear little observational resemblance to their more standard counterparts.These include SN2000cx (Li et al.2001;Candia et al.2003),SN2001ay (Phillips et al.2003),SN2002cx(Li et al.2003), and SN2002ic(Deng et al.2004).These extreme events are easily identified through their premax-imum peculiar spectra,Hydrogen emission,and high expansion velocities.Spectral-feature velocities:The diversity in the velocity of the6100˚A SiII feature atfixed epochs has been noted(Branch&van den Bergh1993; Hatano et al.2000).Garavini et al.(2004)and Benetti et al.(2004)have examined the velocity as a function of supernova phase andfind that large subset of objects tightly cluster within a103 km s−1range for any given epoch.A smaller sub-set with much higher velocity dispersion can be partially distinguished through accurate measure-ments of the SiII feature velocity.Spectral-feature velocity evolution:Benetti et al.(2004)find that supernovae cluster when parameterized by the rate of change of the SiII feature velocity˙v and luminosity.Resolution of the velocity gradients requires measurement of˙v to a few km s−1d−1from spectra between peak and40SN-frame days after peak brightness.Spectral-line-ratio:At t<−10,the ratio of line depths of SiII(λ6150˚A)and SiII(λ5800˚A),R(SiII) (Nugent et al.1995),has a range greater than0.1. The subpopulation of supernovae with high veloc-ity gradients also have distinct R(SiII)evolution; they sharply decrease until t=−5andflatten out whereas other supernovae show no evolution for the same time range(Benetti et al.2004).Light-curve evolution:There are a series of supernovae that exhibit systematic deviations in light-curve shape and color(e.g.Hamuy et al. 1996;Richmond et al.1995;Krisciunas et al.2003; Pignata et al.2004).The ranges displayed in the optical light curves can be summarized as follows: 1mag10days before maximum and0.2mag5 days before maximum,0.1mag20-30days after maximum,and0.2-0.3mag60days after maxi-mum.Color:There is evidence that color is a second parameter correlated with peak magnitude(Tripp 1998;Saha et al.1999;Tripp&Branch1999;Par-odi et al.2000).Dust extinction and intrinsic su-pernova color can be distinguished as supernovae get brighter in I as V−I color becomes red,the opposite effect from dust.Color measurements whose propagated uncertainties in the extinction correction are less than the intrinsic B peak mag-nitude dispersion correspond to B−V measured to0.07mag and V−I to0.5mag.Polarization:Normal-and broad-light-curve supernovae have demonstrated varying degrees of polarization(Howell et al.2001).Detection of po-larization is extremely difficult for all but the near-est supernovae and is unrealistic to require in any cosmological survey.Spectroscopy may then serve as a proxy for polarization measurements through their correlation with high and quickly evolving SiII velocities.The SNAP instrumentation suite is de-signed to provide the data necessary for the subclassification process.SNAP will ob-tain broadband photometry over the full supernova-frame optical region,withfine light-curve sampling tuned to natural su-pernova time scales.The SNAP spectro-graph also covers the supernova-frame op-tical region with resolution tuned to the widths of the supernova features.We expect that any residual luminosity and color biases will be smaller than the dispersion observed in the local supernova sample since this represents heterogeneous and diverse supernova-progenitor environments(Branch2001).This assumption will be tested by intensive precur-sor supernova-characterization experiments and SNAP itself.3.1.2.K-correctionA given observing passband is sensitive to dif-ferent supernova-rest-frame spectral regions.K-corrections are used to put these differing photom-etry measurements onto a consistent rest-frame passband(Kim,Goobar,&Perlmutter1996;Nu-gent,Kim,&Perlmutter2002).The SNAP filter-set number,density,and shapes are tuned to give<0.02mag dispersion for the full catalog of currently available SN Ia spectra(Davis et al.2004).The situation will improve further for the confined analysis of supernova subsamples with the expanded spectral library provided by on-going surveys and SNAP itself.3.1.3.Galactic ExtinctionExtinction maps of our own Galaxy are uncer-tain by∼1–10%depending on direction(Schlegel, Finkbeiner,&Davis1998).Supernovafields can be chosen toward the low-extinction Galactic caps where uncertainty can then be controlled to< 0.5%in brightness.These levels of uncertainty have negligible effect on the measurement of w0 and w a(Kim&Miquel2005).Spitzer obser-vations will allow an improved mapping between color excesses(e.g.of Galactic halo subdwarfs in the SNAPfield)and Galactic extinction by dust (Lockman&Condon2005).3.1.4.Cross-Passband CalibrationUncertainties in calibration are one of the im-portant limiting factors in probing the dark energy with supernovae.Distance measurements funda-mentally rely on the comparison offluxes in dif-ferent passbands:for determining the relative dis-tances of supernovae at different redshifts and for color measurements for determining the dust ab-sorption of a single supernova.The relationship between passband calibration and w0and w a is strongly dependent on the specifics of the cross-band correlations.Simula-tion studies(Kim&Miquel2005)demonstrate the strict fundamental limits in the measurement of dark-energy parameters due to uncorrelated cross-band calibration uncertainty.Significantly larger correlated uncertainties can be tolerated(Kim et al.2004).These studies provide requirements for the SNAP calibration program.3.1.5.Extinction by Host-Galaxy DustExtinction from host-galaxy dust can signifi-cantly reduce the observed brightness of a dis-covered supernova.SNAP’s9-band photom-etry will identify the properties of the ob-scuring dust and gas,and thus the amount of extinction suffered by individual super-novae.Incoherent scatter in dust properties yields no bias but increased statistical uncertainty in the dark-energy parameters(Linder&Miquel 2004).Systematic host-galaxy extinction uncer-tainty can be introduced if an incorrect mean dust-extinction law is used in the analysis.This can be minimized by distinguishing and exclud-ing highly-extincted supernovae from the analysis.To give a quantitative example,sup-pose that the Cardelli et al.(1989)model ac-curately describes host-galaxy extinction and an R V=3.1dust is used in the analysis and the 4400–5900˚A rest-frame color is used to determine A V.We calculate that if drift in the mean of the true dust extinction models is constrained to have 2.4<R V<4.4,the vast majority of supernova which have A B<0.1(Hatano,Branch,&Deaton 1998)would have distance-modulus bias of<0.02 mag.3.1.6.Gravitational LensingInhomogeneities along the supernova line of sight can gravitationally magnify or demagnify the supernovaflux and shift the mode of the super-nova magnitude distribution by<∼3%dependingon redshift(Holz&Linder2005).Gravitational lensing magnification is achromatic and unbiased influx so effectively contributes a statistical uncer-tainty that can be reduced below1%in distance if large numbers(>∼70)of supernovae are ob-tained per0.1redshift bin.The effectiveflux dispersion induced by lensing goes asσ=0.088z (Holz&Linder2005).3.1.7.Non-SN Ia ContaminationOther supernova types are on average fainter than SNe Ia and their contamination could bias their Hubble diagram(Perlmutter et al.1999). Observed supernovae must be positively identi-fied as SN Ia.As some Type Ib and Ic super-novae have spectra and brightnesses that other-wise mimic those of SNe Ia(Filippenko1997),a spectrum covering the defining rest frame Si II6150˚A feature and SII features for ev-ery supernova at maximum will provide a pure sample.3.1.8.Malmquist BiasAflux-limited sample preferentially detects the intrinsically brighter members of any population of sources.The amount of magnitude bias de-pends on details of the search but can reach the level of the intrinsic magnitude dispersion of a standard candle(Teerikorpi1997).Directly cor-recting this bias would rely on knowledge of the SN Ia luminosity function,which may change with lookback time.A detection threshold fainter than peak by at leastfive times the intrin-sic SN Ia luminosity dispersion ensures sam-ple completeness with respect to intrinsic super-nova brightness,eliminating this bias(Kim et al. 2004).3.1.9.Extinction by Hypothetical Gray DustA systematics-limited experiment must ac-count for speculative but reasonable sources of uncertainty such as gray dust.As opposed to normal dust,gray dust is postulated to pro-duce wavelength-independent absorption in opti-cal bands(Aguirre1999;Aguirre&Haiman2000). Although models for gray-dust grains dim blue and red optical light equally,near-infrared light (∼1-2µm)is less affected.Cross-wavelength calibrated spectra extending to wavelength regions where“gray”dust is no longer gray will detect and correct for the hypotheticallarge-grain dust.Numerous observations already severely limit the cosmological effects of such a component(Goobar,Bergstr¨o m,&M¨o rtsell 2002).3.2.Statistical Supernova SampleThe statistical supernova sample appropriate for experiments with the presence of systematic uncertainty has been considered in the Fisher-matrix analysis of Linder&Huterer(2003)and validated with our independent Monte Carlo anal-ysis.They examined the measurement precision of dark-energy parameters as a function of red-shift depth considering2000SNe Ia measured in the range0.1≤z≤z max,along with300low-redshift SNe Ia from the Nearby Supernova Fac-tory(Aldering et al.2002).They concluded that a SN Ia sample extending to redshifts of z∼1.7 is crucial for realistic experiments in which some systematic uncertainties remain after all statisti-cal corrections are applied.Ignoring systematic uncertainties can lead to claims that are too opti-mistic.Statistically,∼2000SNe Ia well-characterized “Branch-normal”supernovae provide systematic-uncertainty limited measurements of the dark-energy parameter w a.These represent the cream, z<1.7supernovae of the∼10000total and ∼4000well-characterized SNAP SNe Ia,that can provide robust cosmological measurements(e.g. non-peculiar,low-extinction).This large sample is necessary to allow model-independent checks for any residual systematics or refined standardization parameters,since the sample will be subdivided in a multidimensional parameter space of redshift, light curve-width,host properties,etc.The large number of lower signal-to-noise light curves from supernovae at z>1.7will provide an extended redshift bin in which to check for consistency with the core sample.We require a statistical measurement uncer-tainty for the peak magnitude corrected for ex-tinction and shape inhomogeneity roughly equal to the current intrinsic magnitude dispersion of supernovae,∼0.15mag.4.Quantification of Dark EnergyExpected measurement precisions of the dark-energy parameters w0and w′(=w a/2)for the SNAP supernova program are summarized in Ta-ble3and shown in Figure4.Since SNAP is a systematics-limited experiment,any improve-ments in our projection of systematic uncertainty will be directly reflected in improvements in our w0–w′measurements.We determine precisions for twofiducialflat universes withΩM=0.3,one in which the dark energy is attributed to a cosmolog-ical constant and the other to a SUGRA-inspired dark-energy model(Brax&Martin2000).Fig.4.—The68%confidence region in the dark-energy parameters forfiducial cosmological con-stant(labeled withΛ)and supergravity(labeled with S)universes.The blue solid curves show the results of the supernova simulation and as-sociated systematic-error model,with a Planck prior on the distance to the surface of last scat-tering,and an assumedflat universe.We define w′≡−dw/d ln a|z=1.See Albert et al.(2005)for constraints including the weak lensing half of the mission.If the universe is taken to be spatiallyflat,the SN data(with Planck prior on the distance to the surface of last scattering)determineΩM to 0.01.The present value of the dark energy equa-tion of state is constrained within0.09and the physically crucial dynamical clue of the equation of state time variation is bounded to within0.19. Note that these constraints are systematics lim-ited;much tighter constraints would be obtained if systematics were ignored.Table3also high-Table3SNAP1-σuncertainties in dark-energy parameters,with conservative systematics for the supernova and the shear power-spectrum measurement from a1000sq.deg.one-year weak-lensing survey.Note:These uncertainties are systematics-limited,not statisticslimited.σΩMσΩwσwσw′SNAP SN;w=−10.020.05······SNAP SN+WL;w=−10.010.01······SNAP SN;σΩM=0.03prior;flat;w(z)=w0+2w′(1−a)···0.030.090.31SNAP SN;Planck prior;flat;w(z)=w0+2w′(1−a)···0.010.090.19 SNAP SN+WL;flat;w(z)=w0+2w′(1−a)···0.0050.050.11Fiducial Universe:flat,ΩM=0.3,SUGRA-inspired dark energyNote.—Cosmological and dark-energy parameter precisions for twofiducialflat universes withΩM=0.3,one in which the dark energy is attributed to a Cosmological Constant and the other to a SUGRA-inspired dark-energy model.The parameter precisions then depend on the choice of data set,priors from other experiments(e.g.Planck measurement of the distance to the surface of last scattering), assumptions on theflatness of the universe,and the model for the behavior of w.SNAP is a systematics-limited experiment so any improvements in our projection of systematic uncertainty will be directly reflected in improvements in our w0–w′measurements.In this paper we define w′≡−dw/d ln a|z=1.SNAP can accumulate a wide-field weak-lensing survey at a rate of1000sq.deg.per year of observation.lights the significant value added by measurements of the shear power spectrum with the complemen-tary SNAP weak-lensing program.The precise,homogeneous,deep supernova data set can alternatively be analyzed in a non-parametric,uncorrelated bin,or eigenmode method(Huterer&Starkman2003;Huterer& Cooray2005).One can also obtain the expansion history a(t)itself,e.g.Linder(2003).5.Project Risks and StrengthsThe proposed experiment is a self-contained su-pernova program which is desensitized to cross-experimental calibration,one of the largest sources of systematic uncertainty.The SNAP instrumen-tation suite provides access to any supernova ob-servable anticipated to be important for reducing uncertainties in supernova distances.The SNAP collaboration is large and diverse, which has allowed for substantial efforts to be sup-ported in science reach,computer framework and simulation,calibration approaches,and photo-detector technology development and testing.Our ongoing R&D efforts have placed us at a point of technological readiness to commence construction of the experiment.The major risk to the SNAP collaboration is that a stretch in the JDEM decision making pro-cess and follow-on project funding will lead to a dissipation of the present efforts as people drift offto other intermediate projects.6.Requisite technology R&DA few areas of the SNAP mission implementa-tion require development to achieveflight readi-ness.No new technologies are required,rather particular instances of the technology as chosen by SNAP require some maturation.At present, the SNAP R&D program is primarily funded by the Department of Energy(DOE),with addi-tional support to collaborators from NSF,NASA, CNES,and CNRS/IN2P3for related activities. The SNAP mission architecture has undergone nu-merous studies(GSFC/IMDC,GSFC/ISAL,and JPL/Team-X),has been reviewed several times by external teams of experts at the request of DOE and NSF,and has been extensively presented and discussed at a variety of international conferences.Thus,SNAP is a relatively well-advanced concept, and the internally self-consistent reference model presented here is now ready for more refined opti-mization.R&D has focused on1)SNAP-specific detector development,both visible and near infrared,2)in-tegralfield unit spectrograph design,3)cold front-end electronics,4)calibration procedures and sup-portingflight hardware,5)achievable telescope point stability studies,6)on-board data handling, and7)achievable telemetry rate studies.All of these areas are maturing at a rapid rate and there appear to be no show stoppers for a SNAP JDEM response.Visible detectors:The visible portion of the im-ager is an array of36silicon CCDs with extended red response and improved radiation tolerance. SNAP will materially benefit from an advanced technology based on fully depleted backside illu-minated high resistivity silicon.The development work is DOE funded and is taking place at LBNL and at commercial foundries.We are also devel-oping custom integrated circuits for the electronic readout.NIR detectors:The NIR portion of the imager requires362kx2k format devices.We are evalu-ating HgCdTe devices available from two vendors. Development work funded by DOE is under way to improve the dark current,read noise,and quan-tum efficiency.We are also exploring InGaAs as a backup photoactive material.One NIR vendor will provide a cold front-end ASIC for their detec-tors.For the other,we are leveraging the work we have done for the CCDs to provide cold front-end ASICs.Spectrograph:This is a simple two-prism de-sign with no technology challenges except its in-tegralfield unit(IFU).An image-slicer IFU with the requisite size and efficiency have been built for ground-based astronomy,and will beflown as part of the JWST NIRSPEC.The image slicer R&D is funded by CNES and CNRS/IN2P3.Telescope:This has been studied by the God-dard/ISAL and four prospective space optics sup-pliers.Two industry study contracts are in place to evaluate the design,manufacturability,and testability of the telescope.Studies and vendor discussions have shown that the pointing stability requirements can be met with today’s spacecraft。

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