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Testing Gravity on Cosmic Scales

Testing Gravity on Cosmic Scales. Edmund Bertschinger, MIT IEU Workshop on Fundamental Physics Ewha University, 19 May 2010. Comparison of observational constraints with predictions from general relativity and viable modified theories of gravity.

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Testing Gravity on Cosmic Scales

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  1. Testing GravityonCosmic Scales Edmund Bertschinger, MIT IEU Workshop on Fundamental Physics Ewha University, 19 May 2010

  2. Comparison of observational constraints with predictions from general relativity and viable modified theories of gravity. R Reyes et al.Nature464, 256-258 (2010) doi:10.1038/nature08857 Zhang et al. 2007

  3. Cosmological Measurements

  4. General Theoretical Considerations(Trust, but verify) General covariance, weak equivalence principle Consistency with solar system tests Perturbed RW metric (large-scale homogeneity and isotropy)

  5. Approaches to Phenomenology Test specific Lagrangian-based models (Tsujikawa talk) or Parameterize the solutions (i.e., the metric)

  6. Example: Solar system tests Brans & Dicke 1961 Parameterized Post-Newtonian metric Eddington 1922, Robertson 1962, Thorne & Will 1971

  7. Easily generalized to Schwarzschild, more parameters Assume free-fall = geodesic motion (Weak Equivalence Principle) Nonrelativistic bodies feel F, relativistic bodies feel F+Y GR: g=1  light deflected twice the “Newtonian” amount

  8. Quantitative tests of GRon solar system scales |g-1| < 2×10-5 on length scales of 10-4 pc Cassini spacecraft Shapiro time delay (Bertotti et al. 2003) w > 40000

  9. Quantitative tests of GRon galactic scales Bolton et al. 2006 PRD Gravitational deflection of light using galaxy-galaxy strong lenses g1 on length scales of 1 kpc

  10. Quantitative tests of GR in cosmology Redshift-Distance relation a= 1/(1+z) Zeroth-order metric: Robertson-Walker K = spatial curvature X = composition parameters (e.g. Wm, Wr, …) Observable: GR:

  11. GR or not GR? Line: GR Points: DGP log10c (comoving distance) log10 z DGP (Dvali et al. 2000, Deffayet et al. 2002) self-accelerating branch: Kowalski et al. 2008

  12. Geometric methods cannot distinguish dark energy from modified gravity Any rDE(a) can be mimicked by suitably modified gravity, e.g. f(R), f(G) Must examine perturbations of RW metric

  13. Super-horizon perturbationsEB 2006; EB & Zukin 2008 Two gravitational potentials F, Y Introduce spatially varying curvature (adiabatic) or composition (equation of state; isocurvature). Coordinate transformation brings metric back to homogeneous form, as causality demands for long wavelengths

  14. Causality:Long-wavelength perturbations evolve like separate Robertson-Walker universes Absent super-horizon forces, long-wavelength perturbations must evolve like separate universes Perturbation Y Closed patch Open patch K<0 K>0 Hubble (or Jeans) Length

  15. Result: Long-wavelength consistency relation for curvature and entropy perturbationseven for modified gravity If dX=0, this leads to conservation of z “outside the horizon”

  16. Sub-horizon physics more complex “Variable G” “Gravitational slip” Parameterize solutions: Cosmological PPN Hu & Sawicki 2007, EB & Zukin 2008, Jain & Zhang 2008, Amin et al. 2008, Amendola et al. 2008, Daniel et al. 2009, …

  17. Key physical quantities: fields m, g(generic in fourth-order gravity) F: Newtonian potential F+Y: Potential for massless particles h=1 in GR without relativistic shear stress m=1 in GR for LCDM sources Optimal tests: Pogosian et al. 2010 (e.g. PCA)

  18. Modified Growth of structure Linder & Cahn 2007: Measure H(a), Wm and d(k,a), deduce m(k,a) Peculiar EOS or modified gravity?

  19. Peculiar velocities Less sensitive to galaxy bias Sensitive to WEP violations (scale-dependent fifth forces) Hui et al. 2009, Koyama et al. 2009 Misalignment of CMB dipole remains unexplained No evidence yet for departures from GR Crook et al. 2010

  20. Weak Gravitational LensingUzan & Bernardeau 2001, Song 2006, Zhang et al. 2007, Song & Dore 2009, Uzan 2009, … Lensing potential: (1+g)F Dark matter potential (growth of structure): F Measure strength of weak lensing, compare with linear growth of structure Nonrelativistic bodies feel F, relativistic bodies feel F+Y GR: g=1  light deflected twice the “Newtonian” amount

  21. Flurry of recent papers combining datasets to test GR Daniel et al. 2010 1002.1962 Bean & Tangmatitham 1002.4197 Zhao et al. 1003.0001 Reviews: Frieman et al. 0803.0982 Caldwell & Kamionkowski 0903.0866 Silvestri & Trodden 0904.0024 Ferreira & Starkman 2009 Science Bean 1003.4468 Jain & Khoury 1004.3294

  22. Many questions remain What are the best parametric and non-parametric statistics for testing GR? (Daniel?) Is there an effective field theory Lagrangian encompassing all the models? (Senatore?) What about isocurvature perturbations? Modified gravity theories have an additional scalar field – what determines its initial conditions? (EB & Silvestri, in prep.)

  23. MIT Department of PhysicsGreen Center for Physics

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