Testing Lorentz invariance of Dark matter with cosmological data

Transcription

1 Testing Lorentz invariance of Dark matter with cosmological data Mikhail Ivanov in collaboration with B. Audren, D. Blas, J.Lesgourges and S. Sibiryakov based on JCAP 10 (2012) 057 [arxiv: ] arxiv:1212.xxxx 6th TRR Winter school Passo del Tonale, December 2012

2 Why Lorentz Violation? Faces of Lorentz breaking: Theory. Better for quantum gravity [Horava, 09] (emergent geometry, Horava-Lifshitz gravity,...) Phenomonology. Puzzles of ΛCDM cosmology: Dark matter and Dark energy. (massive gravity, ghost condensate...) Curiosity. Better pinning down the basic principles.

3 LV in gravity: Einstein-aether theory There is a preferred frame at each point of the space-time set by a dynamical unit vector u µ [Jacobson, Mattingly, 2000].

4 Particular case: khrono-metric theory Aether restricted to be hypersurface-orthogonal: Scalar ϕ(x) - khronon - defines preferred foliation of the space-time

5 Particular case: khrono-metric theory Aether restricted to be hypersurface-orthogonal: Scalar ϕ(x) - khronon - defines preferred foliation of the space-time Khrono-metric theory admits Ultraviolet completion in the context of Horava-Lifshitz gravity (candidate for quantum gravity) [Blas, Pujolas, Sibiryakov, 2010].

6 Particular case: khrono-metric theory Aether restricted to be hypersurface-orthogonal: Scalar ϕ(x) - khronon - defines preferred foliation of the space-time Khrono-metric theory admits Ultraviolet completion in the context of Horava-Lifshitz gravity (candidate for quantum gravity) [Blas, Pujolas, Sibiryakov, 2010]. Number of couplings reduces: α = c 1 + c 4, β = c 1 + c 3, λ = c 2.

7 Particular case: khrono-metric theory Aether restricted to be hypersurface-orthogonal: Scalar ϕ(x) - khronon - defines preferred foliation of the space-time Khrono-metric theory admits Ultraviolet completion in the context of Horava-Lifshitz gravity (candidate for quantum gravity) [Blas, Pujolas, Sibiryakov, 2010]. Number of couplings reduces: α = c 1 + c 4, β = c 1 + c 3, λ = c 2. There is no difference between two theories in the scalar sector!

8 Constraints on LV in gravity h 00 = 2G N m r h 0i = αppn 1 m G N 2 r v i (1 αppn 2 2 (x i v i ) 2 ) r 2 Observations: α1 PPN 10 4, α2 PPN 10 7

9 Constraints on LV in gravity h 00 = 2G N m r h 0i = αppn 1 m G N 2 r v i (1 αppn 2 2 (x i v i ) 2 ) r 2 Observations: α1 PPN 10 4, α2 PPN 10 7 α PPN 1 = 4(α 2β) α PPN 2 = (α 2β)(α λ 3β) 2(λ + β)

10 Constraints on LV in gravity h 00 = 2G N m r h 0i = αppn 1 m G N 2 r v i (1 αppn 2 2 (x i v i ) 2 ) r 2 Observations: α1 PPN 10 4, α2 PPN 10 7 No cancellations: α, β, λ< 10 7 α PPN 1 = 4(α 2β) α PPN 2 = (α 2β)(α λ 3β) 2(λ + β) α PPN 2 vanishes: β= 0, α=λ< 10 4 α PPN 1 vanishes (gravitational wave emission and BBN): α= 2β α, β, λ< 0.01

11 LV in Dark matter: generalized point particle action Newtonian limit: v i, u i small, g 00 = 1 + 2φ

12 LV in Dark matter: generalized point particle action Newtonian limit: v i, u i small, g 00 = 1 + 2φ

13 LV in Dark matter: generalized point particle action Newtonian limit: v i, u i small, g 00 = 1 + 2φ

14 Unscreened regime: enhancement of gravity

15 Screening regime

16 Cosmological perturbations: Screening scale vs. Hubble ρ(x, t) = ρ(t)(1 + δ(x, t))

17 Qualitative matter power spectrum k 1+κ -3+κ k P δ (k) k k -3 Power spectrum in ΛCDM model Power spectrum in LVDM model k 1 1/t eq k max k 2

18 Numerical matter power spectrum 10 5 P δ (k) (α,β,λ)=(2,1,1)*10-2, Y=0.2 (α,β,λ)=(2,1,1)*10-4, Y=0.2 (α,β,λ)=(2,1,1)*10-4, Y=0.02 ΛCDM k (h Mpc -1 ) Figure: Matter power spectrum δ [dm]+[b] = δρ/ρ Rough constraint: Y < 10 2

19 Baryonic Bias (α,β,λ)=(2,1,1)*10-2, Y=0.2 (α,β,λ)=(2,1,1)*10-4, Y=0.2 (α,β,λ)=(2,1,1)*10-4, Y=0.02 δ [b] /δ [dm] k (h Mpc -1 ) Figure: Scale-dependent difference between density perturbations of baryons and dark matter

20 Cosmic Microwave Background 1e-09 8e-10 ΛCDM (α,β,λ)=(2,1,1)*10-2, Y=0.2 (α,β,λ)=(2,1,1)*10-2, Y=0.02 l(l+1)c l /2π 6e-10 4e-10 2e l Rough constraint: Y < 10 2

21 Summary Testing Lorentz invariance of Dark Sector to understand the fundamental properties of the Universe.

22 Summary Testing Lorentz invariance of Dark Sector to understand the fundamental properties of the Universe. Cosmological observations allow us to constrain LV in the Dark Matter sector: same background evolution, but distinct signals for cosmological perturbations. OUTLOOK: Detailed study of parameters, comparison with data, Monte Carlo Markov Chain simulations (in progress)

23 Summary Testing Lorentz invariance of Dark Sector to understand the fundamental properties of the Universe. Cosmological observations allow us to constrain LV in the Dark Matter sector: same background evolution, but distinct signals for cosmological perturbations. Bounds on Lorentz violation in DM at the level 10 2 or better OUTLOOK: Detailed study of parameters, comparison with data, Monte Carlo Markov Chain simulations (in progress)

24 Thank you for your attention!