Eric Linder 21 December 2011

1. The Direction of Gravity Eric Linder 21 December 2011 UC Berkeley & Berkeley Lab Institute of the Early Universe, Korea

2. The 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. Dark Energy as a Teenager 14 years after discovery of the acceleration of the universe, where are we? From 60 Supernovae Ia at cosmic distances, we now have ~600 published distances, with better precision, better accuracy, out to z=1.75. CMBplus external data (H0) points to acceleration. (Didn’t even have acoustic peak in 1998.) BAO detected. Concordant with acceleration. Weak lensing detected. Concordant with acceleration. Cluster masses (ifasystematic) ~1.5 for acceleration. Strong concordance among data: DE~0.73, w~-1.

4. Improving Supernovae EW of supernova spectral features can separate color variation and dust extinction. Nearby Supernova Factory 400 SN Ia with spectra, z=0.03-0.08 >3000 Ia spectra Chotard+ 1103.5300

5. Latest 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, 1105.3470 Suzuki et al, arXiv:1105.3470 Suzuki et al, ApJ 2011, arXiv:1105.3470

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. Are We Done? z>1? w(z)? z<1? (stat+sys) There is a long way to go still to say we have measured dark energy!

8. Chasing 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. Lensing 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-wafor z=0.1-0.6.

10. Time Delays + Supernovae Lensing time delays give superb complementarity with SN distances plus CMB. 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 Factor 4.8 in areaΩm to 0.0044 h to 0.7% w0 to 0.077 wa to 0.26

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

14. Data, 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 conformal diagram SDSS I, II, 2dF 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 bigboss.lbl.gov courtesy of David Schlegel

15. “Greatest Scientific Problem” Redshift “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. Cosmic 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. 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! see P.J.E. Peebles astro-ph/0208037 for inspiration

18. Cosmological 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 Framework Allow parameters to describe growth separate from expansion, e.g. gravitational growth index . Otherwise bias Δwa~8Δ w(a)=w0+wa(1-a) Fit simultaneously; good distinction from equation of state. WL only

20. Beyond GR Functions Test gravity in model independent way. Gravity and growth: Gravity and acceleration: Areandthe same?(yes, in GR) 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. Scale and Time Dependence Padé approximant weights high/low z fairly. Zhao+ 1109.1846 Accurate to ~1% for f(R) and DGP gravity. Shaded – fix to  ; Outline –fitw0,wa Gravity fit unaffected by expansion fit. scale dependent scale independent Outline – fix to GR; Shaded – fit gravity c,s Expansion fit unaffected by gravity fit.

22. 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

23. The Direction of Gravity Understanding whether gravity weakens or strengthens (or is constant) with time is a key clue to the physics of extended gravity. f(R) Look at Gmatter-Gmatter These theories separate in phase space. Today, ΔGm~±0.3 so gravity requirement is 3σ measure requires σ(Gm)~0.1. . GR ★ Gm . GR ★ ★ ★ DGP Linder 2011 Gm

24. 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(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.

25. BigBOSS Leverage BigBOSS+III , BigBOSS+III+WL4000deg2,55/min2 , Current low k, low z low k, high z Glight-1 Glight-1 Gmatter-1 Gmatter-1 Daniel & Linder 2012 high k, high z high k, low z Glight-1 Glight-1 Gmatter-1 Gmatter-1 5-10% test of 8 parameters of model-independent gravity.

26. Paths 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. Galileon Gravity Scalar field π with shift symmetry ππ+c, derivative self coupling, guaranteeing 2nd order field equations. GR Linear coupling Derivative coupling Standard Galileon

28. Expansion & Gravity Solve for background expansion and for linear perturbations – field evolution and gravity evolution. Gmatter Glight Modified Poisson equations. Can study “paths of gravity” evolution of G(a).

29. Galileon Acceleration Accelerates expansion (without potential!) and has de Sitter attractors (w=-1). standard H2 π w linear derivative Rich theory: early DE, phantom, attractors 1+z Appleby & Linder 1112.1981

30. Paths of Gravity Gravity thaws from GR in early universe as G/GN = 1 + bπ Evolution later is not monotonic, as different terms interact. Has de Sitter attractor, with zero slip! Glight Gmatter

31. Galileon Gravity Theory constrained by no-ghost condition and stabilitycs2<0. Forces both linear and derivative couplings to be subdominant at high z. uncoupled linear derivative Great diversity remains. Could G>1 at z~10 help in early massive cluster formation?

32. Summary 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.