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Eric Linder 21 December 2011
UC Berkeley & Berkeley Lab Institute of the Early Universe, Korea
The Direction of GravityThe Direction of Gravity
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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?”.
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Dark Energy as a TeenagerDark Energy as a Teenager
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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
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Suzuki et al, 1105.3470
Suzuki et al, arXiv:1105.3470
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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
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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.
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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)
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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
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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.
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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
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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.
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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)
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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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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
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““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
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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
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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!see P.J.E. Peebles astro-ph/0208037 for inspiration
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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).
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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)
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Test gravity in model independent way.
Gravity and growth:
Gravity and acceleration:
Are and the same? (yes, in GR)
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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).
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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.
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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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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
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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(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”
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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
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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.
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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
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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
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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
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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
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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?
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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. 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.