BIMETRIC GRAVITY AND DARK MATTER Luc Blanchet Gravitation et - PowerPoint PPT Presentation

Rencontres du Vietnam Hot Topics in General Relativity & Gravitation BIMETRIC GRAVITY AND DARK MATTER Luc Blanchet Gravitation et Cosmologie ( G R ε C O ) Institut d’Astrophysique de Paris 14 aoˆ ut 2015 Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 1 / 30

The cosmological concordance model Λ -CDM F 2.8.—The left panel shows a realisation of the CMB power spectrum of the concordance ΛCDM model (red This model brilliantly accounts for: The mass discrepancy between the dynamical and luminous masses of clusters of galaxies The precise measurements of the anisotropies of the cosmic microwave background (CMB) The formation and growth of large scale structures as seen in deep redshift and weak lensing surveys The fainting of the light curves of distant supernovae Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 2 / 30

Challenges with CDM at galactic scales The CDM paradigm faces severe challenges when compared to observations at galactic scales [McGaugh & Sanders 2004, Famaey & McGaugh 2012] Unobserved predictions 1 Numerous but unseen satellites of large galaxies Phase-space correlation of galaxy satellites Generic formation of dark matter cusps in galaxies Tidal dwarf galaxies dominated by dark matter Unpredicted observations 2 Correlation between mass discrepancy and acceleration Surface brightness of galaxies and the Freeman limit Flat rotation curves of galaxies Baryonic Tully-Fisher relation for spirals Faber-Jackson relation for ellipticals All these challenges are mysteriously solved (sometimes with incredible success) by the MOND empirical formula [Milgrom 1983] Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 3 / 30

Challenges with CDM at galactic scales The CDM paradigm faces severe challenges when compared to observations at galactic scales [McGaugh & Sanders 2004, Famaey & McGaugh 2012] Unobserved predictions 1 Numerous but unseen satellites of large galaxies Phase-space correlation of galaxy satellites Generic formation of dark matter cusps in galaxies Tidal dwarf galaxies dominated by dark matter Unpredicted observations 2 Correlation between mass discrepancy and acceleration Surface brightness of galaxies and the Freeman limit Flat rotation curves of galaxies Baryonic Tully-Fisher relation for spirals Faber-Jackson relation for ellipticals All these challenges are mysteriously solved (sometimes with incredible success) by the MOND empirical formula [Milgrom 1983] Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 3 / 30

Challenges with CDM at galactic scales The CDM paradigm faces severe challenges when compared to observations at galactic scales [McGaugh & Sanders 2004, Famaey & McGaugh 2012] Unobserved predictions 1 Numerous but unseen satellites of large galaxies Phase-space correlation of galaxy satellites Generic formation of dark matter cusps in galaxies Tidal dwarf galaxies dominated by dark matter Unpredicted observations 2 Correlation between mass discrepancy and acceleration Surface brightness of galaxies and the Freeman limit Flat rotation curves of galaxies Baryonic Tully-Fisher relation for spirals Faber-Jackson relation for ellipticals All these challenges are mysteriously solved (sometimes with incredible success) by the MOND empirical formula [Milgrom 1983] Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 3 / 30

Mass discrepancy versus acceleration Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 4 / 30

Baryonic Tully-Fisher relation [Tully & Fisher 1977, McGaugh 2011] � 1 / 4 where a 0 ≃ 1 . 2 × 10 − 10 m / s 2 is very � We have approximately V f ≃ G M b a 0 close (mysteriously enough) to typical cosmological values � a Λ = c 2 Λ a 0 ≃ 1 . 3 a Λ with 2 π 3 Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 5 / 30

Modified Poisson equation [Milgrom 1983, Bekenstein & Milgrom 1984] � g � � � µ = − 4 π G ρ baryons with g = ∇ U ∇ · g a 0 � �� � MOND function µ Newtonian regime g ≫ a 0 1 MOND regime g ≪ a 0 g 0 a 0 The Newtonian regime is recoved when g ≫ a 0 In the MOND regime g ≪ a 0 we have µ = g + O ( g 2 ) a 0 Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 6 / 30

Modified gravity theories Generalized Tensor-Scalar theory (RAQUAL) [Bekenstein & Sanders 1994] 1 Tensor-Vector-Scalar theory (TeVeS) [Bekenstein 2004, Sanders 2005] 2 Generalized Einstein-Æther theories [Zlosnik et al. 2007, Halle et al. 2008] 3 Khronometric theory [Blanchet & Marsat 2011, Sanders 2011, Barausse et al. 2015] 4 Bimetric theory (BIMOND) [Milgrom 2012] 5 These theories contain non-standard kinetic terms parametrized by an arbitrary function which is linked in fine to the MOND function In some cases they have stability problems associated with the fact that the Hamiltonian is not bounded from below [Clayton 2001, Bruneton & Esposito-Far` ese 2007] Generically they have problems to recover the cosmological model Λ -CDM at large scales and the spectrum of CMB anisotropies [Skordis, Mota et al. 2006] Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 7 / 30

Modified gravity theories Generalized Tensor-Scalar theory (RAQUAL) [Bekenstein & Sanders 1994] 1 Tensor-Vector-Scalar theory (TeVeS) [Bekenstein 2004, Sanders 2005] 2 Generalized Einstein-Æther theories [Zlosnik et al. 2007, Halle et al. 2008] 3 Khronometric theory [Blanchet & Marsat 2011, Sanders 2011, Barausse et al. 2015] 4 Bimetric theory (BIMOND) [Milgrom 2012] 5 These theories contain non-standard kinetic terms parametrized by an arbitrary function which is linked in fine to the MOND function In some cases they have stability problems associated with the fact that the Hamiltonian is not bounded from below [Clayton 2001, Bruneton & Esposito-Far` ese 2007] Generically they have problems to recover the cosmological model Λ -CDM at large scales and the spectrum of CMB anisotropies [Skordis, Mota et al. 2006] Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 7 / 30

Dielectric analogy of MOND [Blanchet 2007] In electrostratics the Gauss equation is modified by the polarization of the dielectric (dipolar) material ∇ · E = ρ e + ρ polar � � = ρ e e ∇ · (1 + χ e ) E ⇐ ⇒ ε 0 ε 0 � �� � D field Similarly MOND can be viewed as a modification of the Poisson equation by the polarization of some dipolar medium � g � � � � � ρ b + ρ polar ∇ · µ g = − 4 π G ρ b ⇐ ⇒ ∇ · g = − 4 π G a 0 � �� � dark matter The MOND function can be written µ = 1 + χ where χ appears as a susceptibility coefficient of some dipolar DM medium Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 8 / 30

Dielectric analogy of MOND [Blanchet 2007] In electrostratics the Gauss equation is modified by the polarization of the dielectric (dipolar) material ∇ · E = ρ e + ρ polar � � = ρ e e ∇ · (1 + χ e ) E ⇐ ⇒ ε 0 ε 0 � �� � D field Similarly MOND can be viewed as a modification of the Poisson equation by the polarization of some dipolar medium � g � � � � � ρ b + ρ polar ∇ · µ g = − 4 π G ρ b ⇐ ⇒ ∇ · g = − 4 π G a 0 � �� � dark matter The MOND function can be written µ = 1 + χ where χ appears as a susceptibility coefficient of some dipolar DM medium Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 8 / 30

Dipolar dark matter (DDM) [Blanchet & Le Tiec 2008; 2009] Attempt at implementing in a relativistic way the dielectric analogy of MOND 1 The DDM action in standard general relativity is � � � d 4 x √− g + J µ ˙ S DDM = − ρ ξ µ − V ( P ⊥ ) ���� CDM Interaction term couples the matter current J µ = ρu µ to a vector field ξ µ called the dipole moment Potential term V built from the norm of the polarization field P ⊥ = ρ ξ ⊥ and projected orthogonally to the four-velocity u µ The only physical components of the dipole moment are those orthogonal to 2 the four-velocity, hence the dipole moment vector is space-like Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 9 / 30

Dipolar dark matter (DDM) [Blanchet & Le Tiec 2008; 2009] V Newtonian regime Λ 8π MOND regime P 0 a 0 The potential V is phenomenologically determined through third order ⊥ + 16 π 2 V = Λ � � 8 π + 2 π P 2 P 3 P 4 ⊥ + O ⊥ 3 a 0 The natural order of magnitude of the cosmological constant Λ is comparable with a 0 namely Λ ∼ a 2 0 in good agreement with observations Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 10 / 30

Agreement with Λ -CDM at cosmological scales In a cosmological perturbation around a FLRW background the space-like dipole moment must belong to the first-order perturbation ξ µ ⊥ = O (1) The stress-energy tensor reduces to T µν = T µν DE + T µν DDM where the DDM takes the form of a perfect fluid with zero pressure DDM = ε u µ u ν + O (2) T µν where ε = ρ − ∇ µ P µ ⊥ is a dipolar energy density The dipolar fluid is undistinguishable from standard Λ -CDM at the level of first-order cosmological perturbations Luc Blanchet (IAP) Bimetric Gravity and DM Rencontres du Vietnam 11 / 30