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Modified Gravity

Modified Gravity. Takeshi Chiba Nihon University. Why?. Why?. 1. A theory predicts the modification!: Scalar-Tensor Gravity 2. The Nature of Dark Matter is unkown: MOdified Newtonian Dynamics(MOND) 3. The Nature of Dark Energy is completely unkown: F(R) type gravity

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Modified Gravity

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  1. Modified Gravity Takeshi Chiba Nihon University

  2. Why?

  3. Why? 1. A theory predicts the modification!: Scalar-Tensor Gravity 2. The Nature of Dark Matter is unkown: MOdified Newtonian Dynamics(MOND) 3. The Nature of Dark Energy is completely unkown: F(R) type gravity We simply do not know the correct gravity theory in the large (and small) scale

  4. Gravity is Probed at … 10-3cm 1AU 1kpc 1Mpc 1000Mpc large extra dimensions? MOND? Modified Gravity?

  5. Modified Gravity I • Theory Motivated: String theory → Scalar-tensor Gravity If dilaton is (almost) massless, then cosmology and gravity can be different (time varying G) Brans-Dicke parameter: ω0 > 20000 (Cassini satellite,2004)

  6. Scalar-Tensor Cosmology • Scalar-Tensor Gravity • Consequence: Varying G • Constraints: z=1010 (BBN) -0.15<(GBBN-G0)/G0<0.21 (Copi-Davis-Krauss,2004) z=0 (LRR) dG/dt/G<4x10-13 yr-1 What else?

  7. Scalar-Tensor Cosmology • z=1100(CMB) (Nagata-TC-Sugiyama,2004) Effect of G • Projection effect(first acoustic peak, H-1 ) • Shift of zero point of oscillation(Bh2 ) • Diffusion damping(D H-1lmfp ) (damping factor:exp(-2/D2) ) • Decay of gravitational potential (0, ISW)

  8. Nagata-TC-Sugiyama(2002)

  9. Grecom-G0/G0<0.05 (Nagata-TC=Sugiyama,2004)

  10. Scalar-Tensor Cosmology • Scalar-Tensor Gravity • Consequence: Varying G • Constraints: z=1010 (BBN) -0.15<(GBBN-G0)/G0<0.21 (Copi-Davis-Krauss,2004) z=1100 (CMB) (Grecom-G0)/G0<0.05 z=0 (LRR) dG/dt/G<4x10-13 yr-1

  11. Modified Gravity II • Observation motivated(Phenomenology?) Flat rotation curve 　 → MOdified Newtonian Dynamics (MOND)(Miligrom,1986): alternative to dark matter v is constant at large scale ( (v2/r)2/a0=GM/r2 )

  12. MOND Problems(so far): no relativistic formulation 　　← ✖light propagation(gravitational lensing) ✖ large scale structure ✖ cosmology (only recently) relativistic formulation by Bekenstein(2003): vector-scalar-tensor gravity

  13. MOND Bekenstein’s Tensor-Scalar-Vector theory for MOND

  14. MOND • CMB and LSS by Bekenstein’s model (Skordis et al.,2005): consistent with obs.(WMAP,SDSS) if neutrino is massive (~0.17) (← first peak location)

  15. MOND • CMB peaks: sensitive to baryon and dark matter B h2(shift of zero point of oscillation) → first peak height  second peak height  Mh2  (increases the depth of potential well decreases radiation relative to matter(ISW)) → first peak height  second peak → third peak height 

  16. MOND • trouble with higher (second and third) peaks of CMB(Slosar-Melchiorri-Silk,2005) (←Silk damping for baryons) WMAP/Boomerang WMAP

  17. Modified Gravity III • Recent acceleration of the Universe (SNIa) 1.Dark energy: modify RHS of Einstein equation 2.Modify LHS instead ⇒ Modified gravity modification should be significant only recently →1/R gravity (Carroll et al., 2003)

  18. Rise and Fall of 1/R Gravity • F(R) gravity is equivalent to Scalar-Tensor Gravity(Higgs,Whitt,Wands,Chiba): Scalar-tensor with vanishing Brans-Dicke parameter: ω=0 can be in conflict with solar system experiments (ω>20000, Cassini satellite) if Brans-Dicke scalar is (almost) massless This is the case for 1/R gravity :m ~ H0

  19. Rise and Fall of 1/R Gravity • 1/R gravity modifies gravity not only at large scales but also at local scale Einstein ずれ 1/R scale

  20. So much ado… • F(R,P,Q) gravity?(Carroll et al.,2004) P=RabRab,Q=RabcdRabcd → higher derivative (4th order) theory → Ghosts (Stelle 1977,Nunes,Chiba) propagator: cross coupling: The situation is much worse!!

  21. But… • This does not mean all attempts at modifying gravity in the large scale are in trouble (eg. DGP model) • We simply do not know the correct gravity theory in the large (and small) scale （→cosmological PPN formalism?)

  22. Gravity is Probed at … 10-3cm 1AU 1kpc 1Mpc 1000Mpc large extra dimensions? MOND? Modified Gravity? ガモフの飛躍！（100億年→3分間）

  23. PPN(Parameterized Post-Newtonian) • PPN formalism: • expand the metric around the Minkowski up to post-Newtonian order ( (v/c)^4 ) • parametrize possible form of the metric without specifying the gravitational theory • solve the motions of planets and light using the metric and compare them with the observations • | - 1|<4.4 x 10-5 (Cassini,2003), | - 1|< 2.3 x 10-4 (LLR,2004)

  24. Cosmological PPN(or constructing approximate geometry of the universe) • Newtonian gauge: • Cosmological (,x): • Lessons from scalar-tensor gravity: for large  and  is constant if  H-1

  25. ~2 ~ 2/2 nonlinear  post Newton linear Newton ~H

  26. Cosmological PPN(or constructing approximate geometry of the universe) Cosmological metric (valid for   H-1)  Bad: a() is model dependent (H())  Good: (once H is specified) we only have to solve the same linear equations What about  ? -> second order perturbation

  27. But… • This does not mean all attempts at modifying gravity in the large scale are in trouble (eg. DGP model) • We simply do not know the correct gravity theory in the large (and small) scale （→cosmological PPN formalism?) • In this respect, various consistency checks among cosmological observations are important (eg. growth rate, H via lensing and SNIa)

  28. Ishak,Upadhye,Spergel(2005) see also Knox,Song,Tyson(2005)

  29. Searching for alternatives is important • to reinforce the evidence for DM and DE • to check the internal consistency of cosmological data (→ understand systematics)

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