Eric Linder 28 February 2011

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Eric Linder 28 February 2011

UC Berkeley & Berkeley Lab Institute of the Early Universe, Korea

Model Independent Model Independent Tests of Cosmic GravityTests of Cosmic Gravity

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Reality CheckReality 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!

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Higher Dimensional DataHigher Dimensional Data

Cosmological Revolution:

From 2D to 3D – CMB anisotropies to tomographic surveys of density/velocity field.

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Growth SurveysGrowth 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

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Mapping Structure in 3DMapping Structure in 3D

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

We need much better galaxy data to test growth/gravity. Future large scale redshift surveys can give this information – they will be gravity machines!

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Future DataFuture Data

Conformal diagram of Universe

SDSS I, II

BOSS (SDSS III)

BigBOSS 18 million galaxies z=0.2-1.5

600,000 QSOs z=1.8-3

courtesy of David Schlegel

BigBOSS:Ground-Based Stage IVDark Energy Experiment

2dF2dF

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Cosmological FrameworkCosmological 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.

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Gravitational FrameworkGravitational 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.

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Testing GravityTesting 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).

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Parameterizing GravityParameterizing 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.

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2 x 2 x 2 Gravity2 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.

Bin in k and z:

Model independent “2 x 2 x 2 gravity”

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Tests with Current DataTests with Current Data

Good constraints on potential (G), poor on growth (V). Add temperature-galaxy (Tg), galaxy-galaxy (gg) correlations.

95% cl No Tg,gg

uses CFTHLS uses COSMOS

Constraints at high k improve.

V still poorly constrained.

CFHTLS systematic.

with Tg,gg

CMB (WMAP7) SN (Union2) WL (CFHTLS)

Daniel et al 2010

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Future Data LeverageFuture Data Leverage

low k, low zlow k, high z

high k, low zhigh k, high z

BigBOSS (gg) + Planck CMB + Space SN

Factor of 10-100 improvement; 5-10% test of 8 parameters of model-independent gravity.

Daniel & Linder 2010

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ProgressProgress

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?

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de Putter & Linder JCAP 2008

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Phase SpacePhase Space

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

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Types of GravityTypes 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

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Gravity DynamicsGravity 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.

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How Well to Test GravityHow 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!

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Gravity Phase SpaceGravity Phase Space

DGP

f(R)

(Could also compare postGR to G≠1 dark energy models, cf Song++1001.0969).

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Gravity Phase SpaceGravity 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).

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Distinguishing ClassesDistinguishing 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.

.

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Gravity RequirementGravity 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.

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Detail: Scalaron MassDetail: 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 (thawerfreezer). Heads back to (1,0).

Fit form M(a)=M1a-s+M★ is excellent fit.

M(a)/M0

Appleby 2011

Hu & Sawicki

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Detail: Scalaron MassDetail: 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 is k-independent today. Tsu09

AW10

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SummarySummary

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 !