Dark Matter. Testing Lorentz invariance of. Kavli IPMU, Sergey Sibiryakov (INR RAS, Moscow)

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1 Testing Lorentz invariance of Dark Matter Sergey Sibiryakov (INR RAS, Moscow) with Diego Blas, Mikhail Ivanov, Benjamin Audren, Julien Lesgourgues Kavli IPMU, 2013

2 Our Universe is dark

3 Dark matter: present status Theory Plenty of candidates: neutralinos, gravitinos, sterile neutrinos, axions, wimps, wimpzillas,... Experiment Nothing: no direct / indirect detection Only information from gravitational interactions: DM clusters as non-relativistic dust Can we learn more?

4 The key principle since 1905: Lorentz invariance Consider dispersion relation of a particle E 2 = m 2 + c 2 p 2 + n>1 a n p 2n LI c =1,a n =0 Experimental bounds on deviations from LI ( ) c Standard Model gravity dark matter ???

5 Digression 1 Theoretical motivations for deviation from LI May be a consequence of quantum gravity (emergent geometry, Horava-Lifshitz gravity,...) Infrared modifications (e.g. massive gravity, ghost condensation,...)

6 Digression 1I If DM is directly detected very strong bounds on LV SM DM SM SM DM SM cf. Bovy, Farrar 2009 Carroll et al NB. These bounds are model-dependent

7 Dark matter is non-relativistic. Impossible to probe whether it is Lorentz invariant or not? Yes, it is possible! Violation of LI new gravitational degrees of freedom additional attraction between DM particles violation of the equivalence principle enhanced growth of structures

8 Consider the following pattern of Lorentz symmetry breaking SO(3, 1) SO(3) rotations Einstein - aether model Jacobson, Mattingly, 2000 At each point of the space-time there is a preferred frame set by a dynamical unit vector u µ - aether S = M 2 P 2 d 4 x g R + K µ µ u u + l(u µ u µ 1) Lagrange multiplier: enforces unit norm K µ c 1 g µ g + c 2 µ + c 3 µ + c 4 u µ u g

9 Variation: khrono-metric model Blas, Pujolas, S.S., 2010 Aether restricted to be hypersurface-orthogonal: (x) Scalar space-time u µ = µ ( ) 2 - khronon - defines preferred foliation of the preferred time Number of couplings reduced: = c 1 + c 4, = c 1 + c 3, = c 2 NB. Can be embedded into Horava-Lifshitz gravity (candidate for quantum gravity)

10 Constraints from the visible sector LI of the Standard Model no direct coupling of aether to visible matter, interaction only through gravity Post-Newtonian corrections in the Solar System v r h 00 = 2G N m r h 0i = P P N G N m r vi P P N 2 2 (x i v i ) 2 r 2 observations: P P N , P P N

11 P P N 1 = 4( 2 ) P P N 2 = no cancellations P P N 2 vanishes when = 0, = both vanish if ( 2 )( 3 ) 2( + ),, ,, 10 4 = 2 from gravitational wave emission and BBN,, 0.01

12 LV DARK MATTER

13 Generalized point particle action S pp = m ds = Connection to the dispersion relation: m ds f(u µ v µ ) dx µ ds p i = L V i E = p i V i L E 2 = m 2 + (1 + )p 2 f = 1+ (u µv µ ) (u µv µ ) 2 1 2

14 S pp = m ds = Newtonian limit: v i, u i -- small, g 00 = S = Generalized point particle action d 4 x M 2 P + M 2 P c 1 2 u i u i + m ds f(u µ v µ ) d 4 x (v i ) 2 2 dx µ ds Y (ui v i ) 2 2 DM density modified inertial mass = violation of the equivalence principle effective potential for aether in matter m 2 eff f (1) Y M 2 P c 1

15 F F L < M 2 P c 1 Y 1/2 F = F N (1 Y ) Accelerated Jeans instability, = Y 1 Y density contrast

16 v 2 F F u L > M 2 P c 1 Y 1/2 u v 1 F = F N screening of the additional force chameleon-type mechanism Standard Jeans instability 2/3 NB. Standard homogeneous cosmology

17 Screening scale vs. Hubble (b) k Y /a 1/2 ah k, momentum k 2 1/t eq k 1 H 0 (a ) (b ) (a) (c) (c ) t eq t 0 t, conformal time k 2 Y 3H2 0 dmy ( + )(1 Y )

18 Relativistic cosmology Gµ MO LOG 1 m 1 f luid 1 aether = 2 Tµ + 2 Tµ + 2 Tµ + gµ MP MP MP baryonic matter minimally coupled to gravity ÍA de las obs erv aci one sd ((0re. el C 2 so WM 5ludc W M MB AP eiógnr A edee P r.2e5s oglruat dio ons)) Background: Homogeneous and isotropic (preferred foliation aligned with CMB frame) ds2 = gµ dxµ dx = dt2 uµ = (u0 (t), 0, 0, 0) = vµ a(t)2 dxi dxi, (t) Friedmann equations almost not modified! rre stre s) ran ula 00 r. añ des os lu z, aco pl a mie nto 2 a 8 Gc = m a 3 1 Gc = 8 MP2 [1 + 3 /2 + /2] From BBN Gc = GN + O(.01)

19 Cosmological perturbations (x, t) (t)(1 + (x, t)) Scalars: All effects summarized in Y f 0 (1) k, momentum k 2 1/t eq k 1 Y H 0 (b) (a ) (b ) (a) Screening scale Hubble (c) super-horizon (c ) screening k Y /a 1/2 ah no screening t eq matter domination t 0 t, conformal time (kt)2 6 k 2 Y apple = s 3H2 0 dm Y ( + )(1 Y ) (kt)2 6(1 Y ) tapple dmy cm (1 Y ) 5

20 Matter power spectrum: qualitative h (k) (k 0 )i (3) (k + k 0 )P (k)k 3 k 1+κ -3+κ k k -3 P δ (k) k Power spectrum in ΛCDM model Power spectrum in LVDM model k 2 Y k 1 1/t eq k max k 2 Y 3H2 0 dm Y ( + )(1 Y ) k 2 = k Y s dm + b

21 P (k) [h 1 Mpc) 3 ] P δ (k) Matter power spectrum: numerical Preliminary Linear CDM Strong enhancement! 10 3 (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 ) Rough constraint Y < 10 2

22 Cosmic microwave background l(l+1)c l /2π 1e-09 8e-10 6e-10 4e-10 2e-10 (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 Preliminary l CDM Y < 10 2

23 Other effects Baryons bias Anisotropic stress 0.1 δ [b] /δ [dm] a b c d (φ-ψ)/φ a b c k [h Mpc -1 ] k [h Mpc -1 ] α β λ Y k Y,0 (h Mpc 1 ) k Y,eq (h Mpc 1 ) a b c d

24 Rough constraint on LV in dark matter: Y < 10 2

25 Summary Developing theoretical frameworks for deviations from LI is important to better understand our Universe Effects of LV in dark matter on cosmology: same background evolution, but distinct signals for (linear) perturbations. Cosmological observations allow to constrain deviations from LI in dark matter at the level 10 2 or better OUTLOOK Study of the parameter space, comparison with data, effects at non-linear scales