1 1

Eric Linder 21 December 2011

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

The Direction of GravityThe Direction of Gravity

2 2

The Direction of GravityThe Direction of Gravity

Cosmic acceleration: Gravity is pulling out not down!

Is gravity (GNewton) constant, or strengthening, or weakening with time?

Does gravity govern the growth of large scale structure exactly as it does for cosmic expansion, or are there more degrees of freedom?

Effect of gravity on light (strong/weak lensing).

Does gravity behave the same on all scales?

Dark energy motivates us to ask “what happens when gravity no longer points down?”.

3 3

Dark Energy as a TeenagerDark Energy as a Teenager

4 4

Improving SupernovaeImproving Supernovae

EW of supernova spectral features can separate color variation and dust extinction.

Chotard+ 1103.5300

Nearby Supernova Factory

400 SN Ia with spectra, z=0.03-0.08 >3000 Ia spectra

5

Suzuki et al, 1105.3470

Suzuki et al, arXiv:1105.3470

5

Latest DataLatest Data

Union2.1 SN Set• Complete SALT2 reanalysis, refitting 17 data sets• 580 SNe Ia (166+414) - new z>1 SN, HST recalib• Fit Mi between sets and between low-high z• Study of set by set deviations (residuals, color)• Blind cosmology analysis!• Systematic errors as full covariance matrix

Suzuki et al, ApJ 2011, arXiv:1105.3470

6 6

Tests for Systematics and Evolution

No significant deviations from mean of Hubble diagram, or (mostly) in residual slope.

No evolution seen in redshift or population tests.

7 7

Are We Done?Are We Done?

w(z)? z>1?

z<1?

There is a long way to go still to say we have measured dark energy!

(stat+sys)

8 8

Chasing Down Cosmic AccelerationChasing Down Cosmic Acceleration

How can we measure dark energy in detail?

A partial, personal view of promising advances:

•Strong lensing time delays

•Galaxy surveys

•Redshift space distortions

•Weak lensing

•CMB lensing

•Testing gravity

•Testing gravity and expansion simultaneously

9 9

Lensing Time DelaysLensing Time Delays

Strong lensing time delays involve distance ratios, which have different parameter dependences than solo distances.

Unusually sensitive to w0, insensitive to Ωm, and positively correlated w0-wa for z=0.1-0.6.

10 10

Time Delays + SupernovaeTime Delays + Supernovae

Lensing time delays give superb complementarity with SN distances plus CMB.

Factor 4.8 in area Ωm to 0.0044 h to 0.7% w0 to 0.077 wa to 0.26

T to 1% for z=0.1, 0.2,… 0.6

SN to 0.02(1+z)mag for z=0.05, 0.15... 0.95

11 11

Time Delays and CurvatureTime Delays and Curvature

If fit for curvature, time delays reduce degeneracy by factor 5. Except for wa, estimates degrade by <30%, and find Ωk to 0.0063.

12 12

Time Delay SurveysTime Delay Surveys

Best current time delays at 5% accuracy, 16 systems. To get to 1%, either improve systematics, increase sample by 1 OOM, or both.

Need 1) high resolution imaging for lens mapping and modeling, 2) high cadence imaging, 3) spectroscopy for redshift, lens velocity dispersion, 4) wide field of view for survey.

Synergy: KDUST (2.5m Antarctica) + LSST/DES. Overlapping southern fields. NIR/visible partnering. SN survey included. Only low redshift z<0.6 needed for lenses.

(Alternate approach through high statistics stacking rather than detailed modeling, e.g. Oguri & Marshall 2010, Coe & Moustakas 2009)

13

Higher Dimensional DataHigher Dimensional Data

Cosmological Revolution:

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

14 14

Data, Data, DataData, Data, Data

As wonderful as the CMB is, it is 2-dimensional. The number of modes giving information is l(l+1) or ~10 million. BOSS (SDSS III) maps 400,000 linear modes. BigBOSS will map 15 million linear modes.

A gravity machine!

N. Padmanabhan

SDSS I, II, 2dF

BOSS (SDSS III)

BigBOSS 18 million galaxies z=0.2-1.5600,000 QSOs z=1.8-3

BigBOSS:Ground-Based Stage IVDark Energy Experiment

courtesy of David Schlegel

conformal diagram

bigboss.lbl.gov

15 15

““Greatest Scientific Problem”Greatest Scientific Problem”

“When I’m playful I use the meridians of longitude and parallels of latitude for a seine, drag the Atlantic Ocean for whales.”

– Mark Twain, Life on the Mississippi

16 16

Cosmic StructureCosmic Structure

Galaxy 3D distribution or power spectrum contains information on:

• Growth - evolving amplitude

• Matter/radiation density, H - peak turnover

• Distances - baryon acoustic oscillations

• Growth rate - redshift space distortions

• Neutrino mass, non-Gaussianity, gravity, etc.

BigBOSS: initial approval for Kitt Peak/NOAO 4m.

arXiv:1106.1706 ; http://bigboss.lbl.gov

17 17

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!see P.J.E. Peebles astro-ph/0208037 for inspiration

18

Cosmological FrameworkCosmological Framework

Comparing cosmic expansion history vs. cosmic growth history is one of the major tests of the cosmological framework.

If do not simultaneously fit then deviation in one biases the other, e.g. looks like non-GR or non-.

Approach 1: Separate out the expansion influence on the growth – gravitational growth index .

Approach 2: Parametrize equations of motion, i.e. Poisson equation and lensing equation – gravity functions Gmatter(k,a), Glight(k,a).

19

Cosmological FrameworkCosmological 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.

WL only

w(a)=w0+wa(1-a)

20

Test gravity in model independent way.

Gravity and growth:

Gravity and acceleration:

Are and the same? (yes, in GR)

20

Beyond GR FunctionsBeyond GR Functions

Tie to observations via modified Poisson equations:

Glight tests how light responds to gravity: central to lensing

and integrated Sachs-Wolfe.

Gmatter tests how matter responds to gravity: central to

growth and velocities ( is closely related).

21 21

Scale and Time DependenceScale and Time Dependence

Padé approximant weights high/low z fairly.

Accurate to ~1% for f(R) and DGP gravity. Zhao+ 1109.1846

scale independentscale

dependent

Shaded – fix to ; Outline – fit w0, wa

Gravity fit unaffected by expansion fit.

Outline – fix to GR ; Shaded – fit gravity c,s

Expansion fit unaffected by gravity fit.

22

de Putter & Linder JCAP 2008

22

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

23 23

The Direction of GravityThe Direction of Gravity

Understanding whether gravity weakens or strengthens (or is constant) with time is a key clue to the physics of extended gravity.

★

★

GR.

Linder 2011

★

★

GR.

Look at Gmatter-Gmatter

These theories separate in phase space.

Today, ΔGm~±0.3 so gravity requirement is 3σ measure requires σ(Gm)~0.1.

Gm

G m

f(R)

DGP

24 24

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(2N2+1) 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”

25

BigBOSS LeverageBigBOSS Leverage

low k, low zlow k, high z

high k, low zhigh k, high z

BigBOSS+III , BigBOSS+III+WL4000deg2,55/min2 , Current

5-10% test of 8 parameters of model-independent gravity.

Daniel & Linder 2012

Gli

ght-1

Gli

ght-1

Gli

ght-1

Gli

ght-1

Gmatter-1

Gmatter-1Gmatter-1

Gmatter-1

26 26

Paths of GravityPaths of Gravity

Scalar field dark energy (and ) have problems with naturalness of potential and high energy physics corrections.

Can avoid both problems by having a purely geometric object with no potential.

Galileon fields arise as geometric objects from higher dimensions and have shift symmetry protection.

They also have screening (Vainshtein), satisfying GR on small scales.

27 27

Galileon GravityGalileon Gravity

Scalar field π with shift symmetry ππ+c, derivative self coupling, guaranteeing 2nd order field equations.

GR

Linear coupling

Standard Galileon

Derivative coupling

28 28

Expansion & GravityExpansion & Gravity

Solve for background expansion and for linear perturbations – field evolution and gravity evolution.

Modified Poisson equations. Can study “paths of gravity” evolution of G(a).

Gmatter

Glight

29 29

Galileon AccelerationGalileon Acceleration

Accelerates expansion (without potential!) and has de Sitter attractors (w=-1).

H2π w

1+z

standard

linear

derivativeRich theory: early DE, phantom, attractors

Appleby & Linder 1112.1981

30 30

Paths of GravityPaths of Gravity

Gravity thaws from GR in early universe as G/GN = 1 + bπ

Evolution later is not monotonic, as different terms interact. Has de Sitter attractor, with zero slip!

Gmatter

Glight

31 31

Galileon GravityGalileon Gravity

Theory constrained by no-ghost condition and stability cs

2<0. Forces both linear and derivative couplings to be subdominant at high z.

linear

uncoupled

derivative

Great diversity remains. Could G>1 at z~10 help in early massive cluster formation?

32 32

SummarySummary

2D to 3D mapping of cosmic structure is major advance.

Measure growth history. Comparison with expansion history opens window on gravity physics. w(a) alone not enough (especially if w=-1): Gmatter, Glight.

Some models have simple phase space evolution: require 10% measurement on Gmatter. Doable! Galileon gravity much richer.

Model independent approach: 2 x 2 x 2 gravity. 5-10% measures possible, e.g. BigBOSS.