1 / 25

Eric Linder 28 February 2011

Model Independent Tests of Cosmic Gravity. Eric Linder 28 February 2011. UC Berkeley & Berkeley Lab Institute of the Early Universe, Korea. Reality Check. Cosmic gravity desperately needs to be tested. Why? 1) Because we can.

flo
Télécharger la présentation

Eric Linder 28 February 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Model Independent Tests of Cosmic Gravity Eric Linder 28 February 2011 UC Berkeley & Berkeley Lab Institute of the Early Universe, Korea

  2. Reality Check Cosmic gravity desperately needs to be tested. Why? 1) Because we can. 2) Because of the long extrapolation of GR from small scales to cosmic scales, from high curvature to low curvature. 3) GR + Attractive Matter fails to predict acceleration in the cosmic expansion. 4) GR + Attractive Matter fails to explain growth and clustering of galaxy structures. First two cosmic tests failed – explore diligently!

  3. Higher Dimensional Data Cosmological Revolution: From 2D to 3D – CMB anisotropies to tomographic surveys of density/velocity field.

  4. Growth Surveys Galaxy surveys in imaging and spectroscopy Weak lensing CMB lensing Crosscorrelations (g-ISW, -d) – deep surveys with overlapping kernel, e.g. Herschel-CMB. Redshift space distortions Next generation gravity surveys: BigBOSS, KDUST, LSST, Euclid, WFIRST

  5. Mapping Structure in 3D We need much better galaxy data to test growth/gravity. Future large scale redshift surveys can give this information – they will be gravity machines! SDSS main galaxy survey ~650,000 galaxies SDSS luminous red galaxies ~100,000 galaxies BOSS red galaxies [now] 1.5 million galaxies courtesy of David Schlegel

  6. Future Data 2dF SDSS I, II BOSS (SDSS III) BigBOSS 18 million galaxies z=0.2-1.5 600,000 QSOs z=1.8-3 BigBOSS: Ground-Based Stage IV Dark Energy Experiment courtesy of David Schlegel Conformal diagram of Universe

  7. Cosmological Framework Comparing cosmic expansion history vs. cosmic growth history is one of the major tests of the FRW framework. • Allow parameters to describe growth separate from expansion, e.g. gravitational growth index . Otherwise bias • Δwa~8Δ • Fit simultaneously; good distinction from equation of state.

  8. Gravitational Framework “To summarize the theory of general relativity in one sentence, it is that spacetime tells matter how to move and matter tells spacetime how to curve.” – Albert Einstein + John Wheeler metric  velocity, density  metric But is metric = metric? Areandthe same?(yes, in GR) Gravity beyond Einstein is generally described by two functions, scale- and time-dependent.

  9. Testing Gravity Look for time variation between bins of redshift z. Look for space variation between bins of wavemode k. No model assumed – model independent approach. Use gravity-density and gravity-velocity parameters: G relates the metric to the density (Poisson+ eq); central to ISW and lensing. V relates the metric to the motion (velocity/growth eq); central to growth ( closely related).

  10. Parameterizing Gravity Many choices of functions and parameterisation (some convergence). G ,V have good complementarity. 2 functions (combination of potentials) Time dependence (z) Space dependence (k) Complementarity between large scale (low k) / small scale (high k), and early (high z) / late (low z) probes.

  11. 2 x 2 x 2 Gravity Bin in k and z: Model independent “2 x 2 x 2 gravity” Why bin? 1) Model independent. 2) Cannot constrain >2 PCA with strong S/N (N bins gives 2N2 parameters, N2(3N2+1)/2 correlations). 3) as form gives bias: value of s runs with redshift so fixing s puts CMB, WL in tension. Data insufficient to constrain s.

  12. Tests with Current Data Good constraints on potential (G), poor on growth (V). Add temperature-galaxy (Tg), galaxy-galaxy (gg) correlations. Daniel et al 2010 Constraints at high k improve. V still poorly constrained. CFHTLS systematic. CMB (WMAP7) SN (Union2) WL (CFHTLS) 95% cl No Tg,gg uses CFTHLS uses COSMOS with Tg,gg

  13. Future Data Leverage BigBOSS (gg) + Planck CMB + Space SN low k, low z low k, high z high k, high z high k, low z Daniel & Linder 2010 Factor of 10-100 improvement; 5-10% test of 8 parameters of model-independent gravity.

  14. Progress Strong complementarity exists by probing G and V. This requires growth (potential, density) and velocity data, e.g. imaging + spectroscopic surveys. Roles for CMB, WL, galaxy surveys (and xcorrelation). Planck, BigBOSS, LSST, KDUST, Euclid, WFIRST. Need expansion probes for other parameters: SN, BAO (probably ok with modGR). WL formula needs modification if change gravity (G2), DM interaction, FRW inhomogeneity. As approach horizon: see HuS07, BZ08, FerrSkor10 5-10% on 8 postGR – but what is theory requiremnt?

  15. Phase Space de Putter & Linder JCAP 2008 For expansion history, valuable classification of thawing / freezing models in w-w phase space. Plus distinct families in terms of calibrated variables w0, wa – accurate in d, H to 0.1%. Caldwell & Linder PRL 2005

  16. Types of Gravity Gravity beyond general relativity must still approach GR in the early universe and the solar systems. 3 classes of achieving this have been identified. Dimensional reduction [DGP] – GR restored below Vainshtein scale r★(M). Strong coupling [f(R), scalar/tensor] – field mass becomes large near large density and freezes out. Symmetron – field decouples as symmetry forces vanishing VEV. On cosmic scales, first and third similar so just consider DGP and f(R). Khoury 2010

  17. Gravity Dynamics Such theories, e.g. DGP and f(R), have G=1. So only V is relevant. Consider its phase space dynamics, just like for w-w of dark energy. All gravity models of interest are thawers, since they start from GR in the early universe. But they can thaw in different directions. Look at V-V.

  18. How Well to Test Gravity For dark energy, we’ve not answered what precision in 1+w needed. Only have a relative requirement: determine w to of order 1+w. For gravity, phase space analysis gives absolute mission requirement!

  19. Gravity Phase Space DGP f(R) (Could also compare postGR to G≠1 dark energy models, cf Song++1001.0969).

  20. Gravity Phase Space For  = d/dln k, s=2 for f(R), and DGP stays along V =0. For time dependence, parametrize scalaron mass as M(a)=M0a-s(see BZ08,Zhao09,ApplebyWel10).

  21. Distinguishing Classes The classes of theories separate from each other in phase space. GR has (V,V )=(1,0). DGP asymptotes to (2/3,0). f(R) goes to (4/3,0)*. They thaw in opposite directions. By today have moved substantially (since acceleration today). The distance between them, allows for distinction in the physics, and gives the gravity requirement for the survey. .

  22. Gravity Requirement Today, big deviation because acceleration strong: VDGP~0.71, VfR~1.33. So ΔV~±0.3 and have absolute gravity requirement: 3σ measure requires σ(V)~0.1. . GR ★ ★

  23. Detail: Scalaron Mass Note f(R) does not really asymptote to (4/3,0), that is just unstable attractor. In future deSitter, R freezes so M freezes. As a>>1, =k/(aM)0, and GR restored (thawerfreezer). Heads back to (1,0). Fit form M(a)=M1a-s+M★is excellent fit. Hu & Sawicki M(a)/M0 Appleby 2011

  24. Detail: Scalaron Mass f(R) trajectory gets k dependence with scale in M(a). For k>>M1~H, k dependence at z~1-3 but little at z=0. Since V is like , explains why  isk-independent today. Tsu09 AW10

  25. Summary 2D to 3D mapping of cosmic structure is major advance. Measure growth history. Comparison with expansion history opens window on gravity physics. Model independent approach: 2 x 2 x 2 gravity. Gravity requirement from 1) Basic physical classes of GR restoration, 2)Phase space evolution of model families – good separation! Need 10% on V. BigBOSS/eqv (+CMB+SN) delivers 10% on G,V !

More Related