Lorentz violation in cosmology why, how and where

Transcription

1 Lorentz violation in cosmology why, how and where Diego Blas w/ B. Audren, E. Barausse, M. Ivanov, J. Lesgourgues, O. Pujolàs, H. Sanctuary, S. Sibiryakov, K. Yagi, N. Yunes Diego Blas, COSMO 12 Beijing

2 Why Lorentz Violation

3 Why Lorentz Violation Why modifying General Relativity? Learning something fundamental about Nature Improve the UV properties of GR New ideas for black hole thermodynamics New ideas for cosmic acceleration Interesting (testable) phenomenology

4 Why Lorentz Violation Why modifying General Relativity? Learning something fundamental about Nature Improve the UV properties of GR New ideas for black hole thermodynamics New ideas for cosmic acceleration Interesting (testable) phenomenology LV paradise for lazy theorists!

5 Why Lorentz Violation Lorentz invariance (LI) is a key ingredient of Particle Physics, Gravity, Dark Sector is it necessary? which are the bounds? Bounds: PPN benefits of violating LI in gravity: quantum gravity (Hořava gravity, CDT, ) new ideas for black holes technically natural alternative to ΛCDM (ΘCDM)

6 How to do it Space-time filled by a preferred time direction Associated to a time-like unit vector u µ t Generic: x Hypersurface orthogonal: Einstein-æther Khronometric u µ u µ =1 Jacobson, Mattingly 01 x µ ' = ' 1 ' = ' 0 Scalar-vector u µ ' '@ ' khronon

7 Gravitational Lagrangian (IR) Ingredients: u µ, g µ Khronometric L GR = L EH + M 2 P µ ' u µ '@ ' g (r µ u µ ) 2 + (u r u µ ) 2 + r µ u r u µ massless spin 2 graviton! 2 = c 2 t k 2, c 2 t = 1 1 extra massless scalar ' = t +! 2 = c 2 k 2, c 2 = + Einstein-æther (generic u µ ): extra term u µ u µ =1 r µ u r µ u Jacobson, Mattingly 01 extra vector polarizations u µ =ū µ + u µ

8 Gravitational Lagrangian (IR) Ingredients: u µ, g µ Khronometric L GR = L EH + M 2 P µ ' u µ '@ ' g (r µ u µ ) 2 + (u r u µ ) 2 + r µ u r u µ massless spin 2 graviton! 2 = c 2 t k 2, c 2 t = 1 1 extra massless scalar ' = t +! 2 = c 2 k 2, c 2 = + Einstein-æther (generic u µ ): extra term u µ u µ =1 EFT with cut-off IR p M P r µ u r µ u Jacobson, Mattingly 01 extra vector polarizations u µ =ū µ + u µ

9 Gravitational Lagrangian (IR) Ingredients: u µ, g µ Khronometric L GR = L EH + M 2 P µ ' u µ '@ ' g (r µ u µ ) 2 + (u r u µ ) 2 + r µ u r u µ massless spin 2 graviton extra massless scalar ' = t + Possible UV completion: Hořava gravity M? < IR! 2 = c 2 t k 2! 2 = c 2 k 2,, c 2 t = 1 1 c 2 = + Einstein-æther (generic u µ ): extra term u µ u µ =1 EFT with cut-off IR p M P r µ u r µ u Jacobson, Mattingly 01 extra vector polarizations u µ =ū µ + u µ

10 Matter Lagrangian (& Tests) Ingredients: u µ, g µ + SM Fields + DM + DE L m = L LI (SM, DM, DE,g µ )+apple SM L LV (SM,g µ,u µ ) +apple DM L LV (DM,g µ,u µ )+apple DE L LV (DE,g µ,u µ ) SM: e.g. uµ u µ@! 2 = m 2 + c 2 k 2 1 c p,n /c < Kostelecky, Liberati, Mattingly,... dynamical explanation? in the following apple SM =0 DM, DE: apple DM, apple DE? to be answered by cosmology

11 Matter Lagrangian (& Tests) Ingredients: u µ, g µ + SM Fields + DM + DE L m = L LI (SM, DM, DE,g µ )+apple SM L LV (SM,g µ,u µ ) +apple DM L LV (DM,g µ,u µ )+apple DE L LV (DE,g µ,u µ ) SM: e.g. uµ u µ@! 2 = m 2 + c 2 k 2 1 c p,n /c < Kostelecky, Liberati, Mattingly,... dynamical explanation? in the following apple SM =0 DM, DE: apple DM, apple DE? to be answered by cosmology

12 Where: GR is modified in UV and IR, there may be traces of LV everywhere! Diego Blas, COSMO 12 Beijing

13 Tests of Gravity Atomic interferometry Torsion balance Nordtvedt effect, Light deviation Lunar laser ranging, Planets (radar) Satellites (Probe B, GPS) m UV modifications M? > 0.1 ev Huge possible improvement if primordial GW are detected (Blas et al. in preparation) Solar system, GWs, cosmology,... Einstein-æther or Kh theory L EH + p g (r µ u µ ) 2 + (u r u µ ) 2 + r µ u r u µ apple DM, apple DE?

14 Theoretical & Solar System Constraints (Kh) Theoretical stability, no ghosts c 2 > 0, c 2 t > 0, 0 < < 2 no graviational Cherenkov c 2 t 1, c 2 1 Solar system once! v! r h 00 = 2G N M r 1! v 10 2 PPN 1 = 4( 2 ) G N apple SM M 2 P (1 /2) imposed: WEP satisfied h 0i = PPN 1 2 G N m r vi PPN 2 = ( PPN 1 PPN 2 )v 2 2 ( 2 )( 3 ) 2( + ) PPN (x i v i ) 2 r 2 Will 05 =2 identical to GR in the Solar System!

15 Gravitational Radiation (Kh) TH & Solar System constraints leave 2 free parameters Kronometric theory derived from situations with weak gravitational fields GWs tests improve both aspects!

16 Expected Astrophysical Effects u µ v µ g p Matter forces are not modified Gravitation modified (coupling between gravitons and æther) Violation of strong equivalence principle (SEP) (Nordtvedt effect) effectively, for strong gravity regimes this produces a coupling matter-æther for point particles! Z S S pp = m dsf(u µ v µ pp = m ds ) Z the orbital equations depend on u µ v µ

17 Expected Astrophysical Effects SEP violation : dipolar radiation expected h G c 3 d (similar phenomenon in scalar-tensor) dt i r G Pi c 3 r, i Z d 3 x x i Will 01 SEP violated: the conserved momentum does not correspond to P i = m 1 v i 1 + m 2 v i 2 Pi ḣ G c 3 r The dipole mode can be seen directly or in the evolution of binaries

18 Gravitational Radiation (Kh & E-æ) Yagi, Blas,Yunes, Barausse StabilityêCherenkov Binary pulsars BBN b c l l 10 StabilityêCherenkov Binary pulsars c+ Combined constraints from WD-NS andconstraints NS-NS systems FIG. 1. (Color online) on the (c, c ) plane in Æther th obtained by combining constraints derived from observations of P PSR J , PSR J , PSR J [45] and PSR J [46]. The areas outside the (allow considerations (light blue), BBN (dark orange) and the combined bi to the values of the coupling constants required for the (Solar system corresponds constraints enforced) zero-sensitivity/weak-field limit. Observe that the new constraints a +

19 LOG LV in Cosmology L ÍA GR 2p = LEH + MP ar. ños lu cop z, lam ie µ 2 2 µ (r uµ ) + (u r uµ ) + rµ u r u Lm = LLI (SM, DM,, gµ ) + SM LLV (SM, gµ, uµ ) + DM LLV (DM, gµ, uµ ) + DE LLV (DE, gµ, uµ ) so bse rva cio nes (0re.2 del so WM 5ludc W CM M AP eiógnr A B P edee r.2e5s oglruat dio ons)) res ) g µ Natural dark energy Blas, Sibiryakov 11 LV effects from the coupling to uµ = u µ + uµ : (i) background u µ modifies the inertial mass 8 2 and H = 3 Gc m with Gc 6= GN (ii) new interaction from uµ gravitons & DM gravitate differently: no equivalence principle and enhanced collapse!

20 LV effects in Perturbations apple DM =0 Kobayashi, Urakawa, Yamaguchi 10 ds 2 = a(t) 2 (1 + 2 )dt 2 ij(1 2 )dx i dx j Faster Jeans instability: DM dom, subhorizon k 2 a 2 = 3H2 (1 + /2+3 /2) 2(1 /2) = 3G N 2G c H 2 ; 00 +2H 0 = k2 a 2 q t G N G c + Solar system constraints (Kh) =2 G N 1= 3( + ) G c 2 + O(2) > 0 Anisotropic stress = O( )

21 Dark matter: 5th force S = M 2 P Z d 4 x h + 2 ui u ii + Z d 4 x apple (v i ) 2 2 Y ( u i v i ) 2 Potential for DM and aether: Y (i) L M 2 P Y 1/2 F = F N L Faster Jeans instability:, = 1 6 " 1 Y 1+ r 25 Y 1 Y Y > 0 # M 2 P 1/2 (ii) L Y L 2/3 F = F N Screening by alignment

22 Matter Power Spectrum h (k) (k 0 )i (3) (k + k 0 )P (k)k 3 Blas, Ivanov, Sibiryakov 12 P (k) [h 1 Mpc) 3 ] P δ (k) More structure and shift CDM Linear 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 )

23 l(l + 1)Cl/2 Cosmic Microwave Background 4k 2 Audren, Blas, Lesgourgues, Sibiryakov 13 + k 2 c 2 s 3 k 2 G N G c c eff s Shift of the peaks, change of zero point of oscillation and amplitude h i ll 0C l = ISW CDM l

24 Cosmological Constraints (Kh) Audren, Blas, Ivanov, Lesgourgues, Sibiryakov to appear Planck, SPT, WiggleZ log 10 ( ) < 2.42 =2 c 2 = + Y apple CDM log 10 (c 2 ) < 1.51 First bound on LI of DM Y<

25 Non-linear scales 5th force halo profiles/shape WEP violation alignments may happen enhanced mode coupling? screening SEP violation tidal disruptions

26 Non-linear scales 5th force halo profiles/shape WEP violation alignments may happen enhanced mode coupling? screening SEP violation tidal disruptions

27 Conclusions Exploring Lorentz violation yields a rich phenomenology with strong theoretical motivations (effective or fundamental) Lorentz violation modifies gravity at every scale (extra massless d.o.f. ' = t + ) Tests in the gravitational sector Short distance modifications: Solar system tests: GW (strong fields): 1 PPN 2 PPN ,. O(.01) M? > 0.1 ev =2 Cosmological constraints (background and perturbations): growth rate + anisotropic stress + screening Effects on the CMB and matter power spectrum,. O(.01) apple DM. O(.01)

28 Next Challenges Non-linear cosmology Better UV properties than GR (e.g. Hořava gravity) Performing a 1-loop calculation (so far only scaling arguments) Black hole (singularities & thermod) Early universe (inflation?) Making Lorentz Invariance emergent in the IR RG flow Nielsen, Picek 83 Bednik, Pujolàs, Sibiryakov 13 SUSY Groot Nibbelink, Pospelov, 04 M P suppression Pospelov, Shang 10