The Nature of Dark Energy and its Implications for Particle Physics and Cosmology

Transcription

1 The Nature of Dark Energy and its Implications for Particle Physics and Cosmology May 3, University of Tokyo Tomo Takahashi Department of Physics, Saga University

2 1. Introduction Current cosmological observations suggest that the universe is accelerating today. 3 Supernova Cosmology Project No Big Bang Knop et al. (23) Spergel et al. (23) Allen et al. (22) Contents of the universe baryon 2 1 Supernovae CMB expands forever recollapses eventually Clusters closed dark matter 25% 5% Ω Λ 7% dark energy -1 open flat Ω [From the web page of SCP] M The present universe is dominated by something dark. In particular, dark energy almost dominates the present universe. However, we have not understood it yet.

3 Plan of this talk 1. Introduction 2. Current constraints and some implications 3. The nature of dark energy affects other aspects of cosmology? 4. Summary

4 2. Current constraints and some implications What is dark energy? Some energy which accelerates the present universe Cosmic acceleration: ä a = 1 6Mpl 2 (ρ + 3P ) a : scale factor ρ : energy density P : pressure If the equation of state w P ρ < 1 3, the universe can be accelerated. (However, wm = for matter and wr = 1/3 for radiation) We need something weird with wx < - 1/3. Dark Energy

5 Parameters characterizing dark energy Equation of state Energy density w X = p X ρ X Ω X = ρ X ρ crit (for a constant equation of state) ρ X (a) = ρ crit Ω X a 3(1+w X ) Dark energy can also fluctuate, thus we need more to characterize DE. affects cosmic density fluctuation (CMB, LSS,...) Speed of sound of DE c 2 s δp δρ σ X ( Anisotropic stress of DE ) rest These quantities can be constrained by observations. Clues for dark energy

6 (First we discuss the effects of the background modification.) Ω X w X Once and are specified, we can know how the universe is accelerated. ä a = ρ crit 6M 2 pl (Ω m a 3 + Ω r a 4 + Ω K a 2 + Ω X a 3(1+w X ) ) ( Or the background evolution) H 2 (a) = H (Ω ) 2 m a 3 + Ω r a 4 + Ω K a 2 + Ω X a 3(1+w X ) Ω X and w X can be constrained by various observations such as Type Ia supernovae (SNeIa) Cosmic microwave background (CMB) Baryon acoustic oscillation (BAO)

7 SNeIa Luminosity distance CMB BAO d L = 1 + z ( Ωk z Ωk S ) dz, H(z )/H [Recent observations: A. G. Riess et al., arxiv:astro-ph/611572; Davis et al., arxiv:astro-ph/7151; Wood-Vasey et al, astro-ph/7141] Acoustic peak position gives the angular diameter distance to last scattering surface Angular diameter distance [Spergel et al., astro-ph/63449; Wang&Mukherjee, astro-ph/6451] Baryon acoustic peak was detected by observing galaxy samples z ~.35. [Eisenstein et al,. ApJ 633, 56, 25] d A = z dz H(z ) l(l+1)c l /2! m-m(mag) ! m =.3,! x =.7 34 SN! m =1.,! x =.! m =.3,! x =. Riess et al. (24) CMB z BAO multipole l w X =-.5 w X =-1. w X =-2.

8 Observational Constraints on the eq. of state For a constant equation of state (and a flat univ.) (SNeIa) (BAO) m-m(mag) ! m =.3,! x =.7 34 SN! m =1.,! x =.! m =.3,! x =. Riess et al. (24) z (CMB) # (all) l(l+1)c l /2! w X =-.5 w X =-1. w X = CMB multipole l [Ichikawa & TT, PRD 73, (26)] BAO # Constraint from the shift parameter (position of acoustic peak)

9 Recent constraints (for a flat universe and a constant equation of state.) Spergel et al (WMAP3), 26 Tegmark et al, PRD74,12357,26. (astro-ph/68632) [WMAP3+other CMB+2dF+SDSS+SN] w X = (with perturbation) [WMAP3+SDSS] w X = (with perturbation) [WMAP3+BAO] w X = (with perturbation) Percival et al, arxiv: [astro-ph] [CMB(theta)+SN(SNLS)+BAO(SDSS+2dF)] [WMAP3+SN(gold)] w X = [WMAP3+SN(SNLS)] (with perturbation) w X = 1.4 ±.89 Wood-Vasey et al, astro-ph/7141 w X = (with perturbation) [SN(ESSENCE)+BAO(SDSS)] w X =

10 Models for an accelerating universe proposed so far Cosmological constant (Λ) (wx = -1) Scaler field Quintessence K-essence (with a non-canonical kinetic term) DGP (Dvali-Gabadaze-Porrati) model f(r) gravity Cardassian model ( (ρ + Bρ n ) ) Ghost condensate H 2 = 1 3M 2 pl (No criterion for the choice of models here.) Too many!

11 Cosmological constant? A naive estimate of Λ in quantum field theory: ρ Λ M 4 pl (1 18 GeV) 4 From cosmological observations: ρ Λ Λ 4 (1 3 ev) 4 M 4 pl/λ ! Numerical coincidence? 1 15 TeV 1TeV 1 15 TeV M planck v EW Λ energy scale v 2 EW/M pl Λ any reason?

12 Dark energy is dynamical? An example: quintessence (a scalar field) Q Tracker type model (the ratio ρ DE /ρ m (ρ rad ) V (Q) = Λ 4+α /Q α V (Q) = Λ 4 exp( λq) constant) [Ratra,Peebles PRD 37,346,1998] [Ferreira,Joyce PRD 58,2353,1998] V (Q) = V [ (Q B) 2 + A ] exp( λq) [Skordis, Albrecht PRD 66,43523,22] V (Q) = ( Λ 4 /Q α) exp(κq 2 ) [Brax,Martin PLB 468,4,1999] cosine type model (Psuedo-Nambu-Goldston boson) V (Q) = Λ 4 (1 cos(q/f Q )) Energy density [Coble,Dodelson,Frieman PRD 55,1851,1997; Viana,Liddle PRD 57,674,1998] (mass scale: m Q H 1 33 ev ) ρ tracker ρ m a 3 Tracker oscillating model V (Q) = Λ 4 [1 + A sin(νq)] exp ( λq) ρ cosine [Dodelson,Kaplinghat,Stewart PRL 85,5276,2] Various models even just for quintessence... scale factor

13 (Too) Many models proposed (but none of them are compelling). Phenomenological approach using observations Key questions: The equation of state is -1 (cosmological constant) or not? The equation of state is time-dependent (dwx /dz = ) or not? Probe the time-dependence of the equation of state wx (z). Although time dependence of wx can be complicated, in most analysis, some simple parametrizations are adopted. (and see dwx /dz )

14 Observational Constraints on the eq. of state II For the time-varying equation of state Assuming a simple model: w X = w + w 1 (1 a) = w + w 1 z 1 + z (A flat universe is assumed.) BAO w X = w + w 1 > CMB SN BAO+CMB+SN [Ichikawa & TT, PRD 73, (26)] cosmological constant case ( w 1 is marginalized.)

15 Observational Constraints on the eq. of state III Another parametrization a q + a q s w(a) = w w 1 a q w 1 + a q sw [Hannestad,Mortsell JCAP49,11,24] w = w 1 = 1 (LCDM: ) Some examples for the evolution of w w =.5 w 1 = 1.5 q =.5, 1, 2, 5, 1 [Hannestad,Mortsell JCAP49,11,24]

16 Observational Constraints on the eq. of state IV Another parametrization [Wetterich PLB 594, 17, 24] w X (z) = w [1 + b log(1 + z)] 2, (LCDM: w = 1, b = ) SN (1σ constraint) (1σ constraint, b is marginalized.) SN+CMB SN+CMB+BAO [Movahed, Rahvar PRD 73, 83518, 26]

17 (Short summary of this part) A cosmological constant is allowed (in almost all analysis). (looks pretty good in some analysis/data set.) Various dark energy models are still allowed. Many candidates for dark energy (accelerating universe) have been proposed, (fortunately/unfortunately) none of them are compelling. ( For dark matter, plausible candidates in particle physics.)

18 In fact, more to be specified to characterize dark energy We also have to specify the perturbation nature of dark energy. Speed of sound of DE Anisotropic stress of DE σ X + 3H c2 a w X σ X = 8 3 α c 2 s δp X δρ X rest. σ X (θ X + h 2 + 3η ) [Hu ApJ 56, 485,1998; Bean&Dore PRD 69,8353,23] [Hu ApJ 56, 485,1998; Koivisto&Mota PRD 73, 8352, 26; Ichiki&TT PRD, astro-ph/73549] : specified by viscosity parameter α Perturbation equations for a general dark energy For density pert., For velocity pert., δ X = (1 + w X ) [ k 2 + 9H 2 (c 2 s c 2 a) ] θ X k 2 3H(c2 s w X )δ X (1 + w X ) h 2 θ X = H(1 3c 2 s)θ X + c2 sk w X δ X k 2 σ X (the prime denotes a derivative w.r.t. the conformal time) where c 2 a p X ρ X = w X w X 3H(1 + w X ). Specified once EoS is given These can affect cosmic density density fluctuation

19 Effects of fluctuation of dark energy 6 Sound speed 6 Anisotropic stress l(l+1)c l /2! c 2 s = 1 "=1 c 2 s "=.1 = c 2 s "=.1 = c 2 s "= = l(l+1)c l /2! "= "=.1 "=.1 "= multipole l multipole l For quintessence (a scalar field with the canonical kinetic term), c 2 s = 1 For example, k-essence (a scalar field with a non-canonical kinetic term), c 2 s 1 Low multipoles of CMB are mainly affected. Even if the eq. of state is same, fluctuation make some difference. Cross-correlation of ISW and LSS may be helpful.

20 Although the sound speed and anisotropic stress themselves cannot be severely constrained, constraints on other quantities can be affected. Constraint on w with different assumptions for and. c 2 s α α=, Cs 2 =1 α=, Cs 2 = WMAP +HST α=, Cs 2 =1 α=, Cs 2 = WMAP +HST+ 2dF probability probability w w [Ichiki&TT PRD, astro-ph/73549] The assumption may cause ~1 % difference.

21 Constraint on w with different assumptions for c 2 s and α. WMAP +HST WMAP +HST +2dF [Ichiki&TT PRD, astro-ph/73549]

22 3. The nature of dark energy affects other aspects of cosmology? Main concern of dark energy research is to figure out what the dark energy is. the nature of dark energy can affect other aspects? Implications for other aspects? (Some examples) Dark energy and mass varying neutrinos Next Takahashi s talk Relic abundance of DM can be affected by quintessence model? The curvature of the universe Primordial fluctuation (spectral index, gravity wave, scalar spectral running)

23 (Example 1) Relic abundance of DM in models with quintessence model In some models of quintessence, the kinetic energy of quintessence can dominate the universe. [Salati PLB 571,121,23; Rosati PLB 57,5,23; Profumo & Ullio JCAP311,6,23; Pallis JCAP 51,15,25] During kinetic energy-dominated phase, ρ φ a 6 Example: V (φ) = M 4 pl exp ( λφ/m pl ) V (φ init ) = 3M 2 plh 2 i 1 BBN "=2.5 1 BBN H i =1 11 GeV Log(!) 5 radiation + matter a 4 a 3 Log(!) 5!5!5!1 H i =1 8 H i =1 1 H i =1 12!1 "=2. "=3. "=4.!15!4!3!2!1 Log(a/a )!15!4!3!2!1 Log(a/a )

24 Relic abundance can be enhanced when DM decouple in kination domination period. Standard case DM decouples during radiation-dominated epoch ( ) H 2 = 1 3Mpl 2 ρ a 4 If DM decouples during Kination domination (kinetic energy dominated epoch) H 2 = 1 3Mpl 2 ρ a 6 dn χ dt + 3Hn χ =< σv > { (n () χ ) 2 n 2 χ } f! = n! T 3 Equilibrium 25 GeV Bino tan"!= 5 Decoupling [Salati PLB 571,121,23] Effect of kination on neutralino decoupling # $ "% # $ "#$#% # $ "# m! /T Earlier decoupling Enhanced relic abundance

25 (Example 2) Effects on the constraint on the curvature of the universe It is usually said that current observations favor a flat universe [Spergel et al., 26]!,!./-!12π),34 2 =;;; <;;; 2;;; 5+6"#78)9:7#( A;B 2B ;C?B ;C2B KK)8'LL)G'M(8 9&(:$8"* Λ >)E!)5##)E7$7 F!5G HI 5H5J /;;;.5.4 WMAP WMAP + SN gold ; The position of the peak The curvature of the universe shifts the peak position. The universe is (almost) flat. (Assuming a cosmological constant as dark energy.) The flatness is robust even if we assume different types of dark energy?

26 The EoS of dark energy also affect the CMB power spectrum. 6 Varying w X. Varying Ω k. 6 l(l+1)c l /2! w=-.6 w=-1. w=-2. l(l+1)c l /2! " k =-.1 " k = " k = multipole l multipole l Degeneracy between EoS of DE and the curvature

27 Constraint on the curvature of the universe Assuming a cosmological constant as dark energy SN BAO A flat universe is favored. CMB ALL [Ichikawa & TT, PRD 73, (26)]

28 Constraint on the curvature of the universe Assuming a constant equation of state w X ( w X is marginalized over.) SN BAO CMB ALL A flat universe is favored even though we do not assume w X = 1 [Ichikawa & TT, PRD 73, (26)]

29 Contours of EoS giving the minimum chi2 for each (Ω m, Ω X ). SN BAO CMB w X =.8 w X = 1 w X = 2 Each observation favors different values of EoS. When all data combined, it gives a flat universe.

30 Constraint on the curvature of the universe Assuming a time-varying equation of state as SN BAO w X = w + (1 a)w 1 = w + z 1 + z w 1 ( w and w 1 are marginalized over.) CMB ALL A flat universe is favored even though we assume a time-varying equation of state. [Ichikawa & TT, PRD 73, (26)] The flatness is robust?

31 Constraint on the curvature of the universe Assuming a time-varying equation of state as w + w 1 w z (for z z ) w X (z) = z w 1 (for z z ) w X ALL redshift z An open universe can be allowed ( Ω k.2 ) for some case in this model. [Ichikawa, Kawasaki, Sekiguchi & TT, JCAP 12, 5(26)]

32 Constraint on the curvature of the universe Assuming a time-varying equation of state as w X (z) = w [1 + b log(1 + z)] 2, 1 [Wetterich PLB 594, 17, 24].8 ALL w X redshift z [Ichikawa & TT, JCAP 2, 1(27)] An open universe can be allowed in this case too.

33 (Example 3) Effects on the constraints on primordial fluctuation The nature of primordial fluctuation is now severely constrained by observations. Spectral index ns : P R k n s 1 Tensor-to-scalar ratio r : r = P T P R Running of the scalar spectral index αs : α s = d ln n s d ln k 6 spectral index 6 tensor mode Running of scalar spectral index 6 l(l+1)c l /2! n s =.95 n s =.9 n s =1 n s =1.5 n s =1.1 l(l+1)c l /2! scalar tensor r=.5 r=1. l(l+1)c l /2! no running alpha=.1 alpha= multipole l multipole l multipole l

34 Effects of dark energy and primordial fluctuation look similar? 3 Sound speed 3 Anisotropic stress l(l+1)c l /2! c 2 s = c 2 s =.1 c 2 s =.1 c 2 s =1 l(l+1)c l /2! "= "=.1 "=.1 "=1 "= multipole l multipole l (w=-.8) 6 Running of scalar spectral index 6 tensor mode l(l+1)c l /2! no running alpha=.1 alpha=.2 l(l+1)c l /2! scalar tensor r=.5 r= multipole l multipole l

35 Dark energy fluctuation and the running of spectral index 6 Running of scalar spectral index 6 Sound speed l(l+1)c l /2! no running alpha=.1 alpha=.2 l(l+1)c l /2! c 2 s = "=1 1 c 2 s "=.1 = c 2 s "=.1 = c 2 s = "= multipole l multipole l 7 l(l+1)c l /2! c s 2 =1, "s = c s 2 =, "s = c s 2 =1, "s =.16 c s 2 =, "s =.16 Degeneracy between the running and the sound speed multipole l

36 Constraint on the scalar spectral index and tensor-to-scalar ratio For some different values of c 2 s and α 1 1 [Ichiki & TT in preparation] (Using MCMC approach).8 Cs 2 = w free Cs 2 =1 w free w = -1 (fixed).8 Cs 2 = w free Cs 2 =1 w free w = -1 (fixed) probability.6.4 probability n s r [WMAP+HST] 6 6 l(l+1)c l /2! n s =.95 n s =.9 n s =1 n s =1.5 n s =1.1 l(l+1)c l /2! scalar tensor r=.5 r= multipole l multipole l The nature of DE can also affect the constraints on the running spectral index.

37 4. Summary Current precise cosmological observations can constrain the equation of state for dark energy, severely in some cases. A cosmological constant is allowed (in almost all analysis), however, various kinds of dark energy can also still be allowed. The nature of dark energy also affects other aspects of cosmology (such as constraints on the curvature, primordial fluctuation,...). Dark energy is one of the most important problems in today s science. We need to keep working on it.