Dark energy constraints using matter density fluctuations

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1 Dark energy constraints using matter density fluctuations Ana Pelinson Astronomy Department, IAG/USP Collaborators: R. Opher (IAG/USP), J. Solà, J. Grande (Dept. ECM/UB) I Campos do Jordão, April 5-30, 009

2 Dark energy and the "cosmological constant problem" Recent observations indicate a "dark energy" ρ hoje Λ 0.7ρ 0 c M 4 Pl. However, there is a big discrepancy when we compare with ρ vac = where M Pl = 1/8πG = GeV is the reduced Planck mass. Actually, if we suppose M SUSY GeV: ρ vac M 4 SUSY 10 1 M 4 Pl. Λ=constant (ΛCDM) problems: 1. Old problem: Why ρ hoje Λ is so small?. Coincidence problem: Why ρ hoje Λ Λ (8πG), has the same order of ρ hoje? Why now? M Dark energy models constrained using matter density fluctuations: 1. A FLRW model with a running Λ [Λ(t)CDM];. The Λ(t)CDM with a extra X component [Λ(t)XCDM].

3 Linear dark matter and dark energy densities perturbations We should consider simultaneous perturbations in: ρ N ρ N +δρ N, p N p N +δp N, g µν = g B µν+h µν U µ N Uµ N +δuµ N, with a gauge invariant non adiabatic pressure perturbation: δp D = c s δρ D + 3Ha (1 + w e)ρ D (c s c a) θ D k, (1) where c s is the effective and c a is the adiabatic sound velocity c a p D ρ D w e = w e a 3 (1 + w e ) [H. Kodama, M. Sasaki, Prog. Theor. Phys. 1984] in terms of the dark energy effective equation of state (EOS) w e p D ρ D.

4 Dark matter and dark energy fluctuations The perturbed equations ( ) δ M = 1 θ M ĥ, ah δ D = (1 + w e) ah { [ 1 + 9a H (c s c a) k θ M = a θ M, ] } θ D ĥ 3 a (c s w e )δ D, θ D = 1 ( ) 3cs θ D + k cs δ D a a 3 H (1 + w, e) ĥ + a ĥ 3H a Ω M δ M = 3H a Ω [ D (1 + 3cs )δ D + 9a H(cs ca) θ ] D, k where ĥ t ( hii a ) and θ N µ (δu µ N ) = i(δu i N), diverge for w e 1(ρ D const.) and c a < 0.

5 Neglecting dark energy fluctuations δ D δρ D /ρ D 0 The growth of the matter fluctuations G(a) δ M (a)/a [ G 7 (a) + 3 ] w e (a) r(a) G (a) + 3 [1 w e (a)] r(a) 1 + r(a) a 1 + r(a) is scale independent (k). The linear scale independent bias" parameter G(a) a = 0 () b = P GG /P MM P GG /(δρ M /ρ M ) (3) should be close to 1 when the galaxies had time enough to correlate with the mass distribution of the Universe. (P GG is given by LSS data and P MM a G (a) is model dependent). The successful standard ΛCDM model predicts b Λ (0) 1 ( 10% accuracy) [S. Cole et al, MNRAS 005]

6 The FLRW model with variable Λ(t) The Friedmann equation is given by: ( ) H ȧ = = 8πG a 3 (ρ M + ρ Λ ), (4) where ρ Λ is motivated by quantum field theory ρ Λ ρ Λ (t) = ρ 0 Λ + 3 ν 8π M P ( H H 0 Energy exchange between the vacuum and matter sectors ). (5) ρ M + ρ Λ = 3Hρ M. (6) [I.L. Shapiro, J. Solà, JHEP 00; PLB 000] The dimensionless parameter ν is defined by ν σ 1 π M MP, (7) M is the effective mass of the heavy particles, bosons/fermions (σ = ±1) M = M Pl ν ν (8)

7 The ΛXCDM model The total dark energy" is composed by: ρ D = ρ Λ + ρ X, p D = p Λ + p X, (9) where ρ Λ = ρ Λ (t) e ρ X = ρ X (t) is a cosmon" component. [J. Grande, J. Solà, H. Štefančić, JCAP 006] The component X is obtained from the total dark energy conservation law where w X is the EOS of the cosmon" w X is considered in one of the following ranges: ρ X + ρ Λ = 3H(1 + w X )ρ X, (10) w X p X ρ X. (11) 1 < ω X < 1/3 (quintessence-like cosmon) or ω X < 1 (phantom-like cosmon).

8 The ΛXCDM and the coincidence problem The total DE density varies in such way that the ratio r(a) Ω D /Ω M can be bounded due to the existence of a maximum r a D a M a parameters values Ν Ν wx 0.5 r XCDM a r CDM a a where the Universe stops expanding [ 1 Ω 0 r(a) = Λ w ] X a 3(w X ɛ) + (Ω0 Λ ν) a 3 Ω 0 M (1 ν) w X ɛ (1 ν) Ω 0 M where r 0 = Ω 0 D/Ω 0 M = 0.7/ and ɛ ν(1 + w X ). + ɛ w X ɛ, (1)

9 F-test" We applied the following test F 1 b (z) bλ (z) to the Λ(t)CDM models, predicting z=0 = 1 G Λ(z) G (z) 0.1, (13) z=0 ν 0.05ν , (14) which is in agreement with different methods and authors. [J. Grande, R. Opher, A. Pelinson, J. Solà, JCAP 007] This condition further constraints the limited 3D region in the parameter space (Ω 0 Λ, w X, ν) of the ΛXCDM model associated with restrictions of nucleosynthesis plus solution of the coincidence problem.

10 3D-region in the parameter space (Ω 0 Λ, w X, ν) for Ω 0 M 0.3 Constraints using nucleosynthesis plus the two restrictions associated with the solution of the coincidence problem gives: Ν Ω X [J.Grande, J.Solà and H.Štefančić, JCAP 006]

11 New 3D-region in the parameter space (Ω 0 Λ, w X, ν) Volume of points allowed by nucleosynthesis bound, coincidence problem" conditions, together with the effective EOS restrict to 1 + ω e(0) 0.3 and the F-test" Ν Ω X [J. Grande, R. Opher, A. Pelinson, J. Solà, JCAP 007]

12 Adiabatic (c s = c a < 0) and non-adiabatic 0 c s 1) perturbation δ D (a) k= k λ s = π c s = c a c s = 0 c s = a The adiabatic perturbations diverge for c s = c a = (a) Ω0 X Ω X (a) (1 + b)(ω X ɛ) a 3(1+ω X ɛ < 0. and when b ν Ω0 M (ω X ɛ) Ω 0 X < 0 (at the crossing w e(a) = 1).

13 Further constraints in the 3D region of the parameter space 0 (b) (c) ω X -1 Ω Λ Ω Λ ν Projections without divergence in δ M. Allowed region gives (w X < 1 and Ω 0 Λ > 0.7) Ω 0 X = 0.7 Ω 0 Λ < 0: (1 + w 0 e ) Ω 0 D = (1 + ω X ) Ω 0 X 1 < w 0 e < 1/3. Final conclusion: The total DE density ρ D behaves effectively as quintessence. [J. Grande, A. Pelinson, J. Solà, arxiv: ]

14 Matter power spectrum log 10 P k h 3 Mpc P k P X k, c S 1 P X k, c S 0.1 a log 10 P k h 3 Mpc P X k,c S 0.1 P X k,c S 1... P X k, D Θ D 0 b P k log 10 k h Mpc log 10 k h Mpc 1 Ω 0 M = 0.3, Ω 0 Λ = 0.8, ν = ν , w X = 1.6; (c S = 0.1; 1) P Λ (k) δ M (k) = A k T (k) g (Ω 0 T ) g (Ω 0 M ) ; A = h 4 Mpc 4 (χ = 0.43) [J. Grande, A. Pelinson, J. Solà, Phys.Rev.D 009]

15 Conclusions If the dark energy is varying in time... The matter density perturbations (as well as the dark energy fluctuations) need to be well defined. The growth of the matter density fluctuations (as well as the matter power spectrum) need to be constrained.

16 Thank you!