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Eric Linder 22 November 2010

UC Berkeley & Berkeley Lab

Institute for the Early Universe Ewha University, Korea

CMB Probes of CMB Probes of Dark EnergyDark Energy

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OutlineOutline

1. Handles on Dark Energy

2. CMB Lensing and CMB-Galaxy Correlations

3. Early, Cold, and Stressed Dark Energy

4. Testing GR with the CMB

5. Is Acceleration Unique?

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Cosmic AccelerationCosmic Acceleration

We observe cosmic acceleration, ä>0 (most directly from supernovae).

Freedman et al 2009

Amanullah et al 2010

with sys

accelerating

decelerating accelerating

decelerating

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Kindergarten CosmologyKindergarten Cosmology

This implies a modification of the Friedmann equations.

So there is either a new source of energy, or a modification of gravity.

These are just energy conservation and Newtons 2nd law:

H2 =

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Dark Energy and ExpansionDark Energy and Expansion

Either way, call it dark energy. For any modification of matter-only Friedmann equation, can always define equation of state.

Acceleration is exactly equivalent to wtotal<-1/3. The EOS wde(z) characterizes the effect of the modification on the expansion.

For example, wde(z)=-1 is the cosmological constant – but many diverse physics give wde(z)~-1.

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Handles on Dark EnergyHandles on Dark Energy

We need more observational handles on dark energy. Consider inflation – in the 1980s people believed it was untestable. Now we explore:

• Tilt and running

• Tensor modes (GW)

• Non-Gaussianity

• Topological defects/relics

Tilt and running are like w and w – the other quantities arise from perturbations, basically spatial variation in addition to time variation.

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Microphysics of Dark EnergyMicrophysics of Dark Energy

Spatial variation of dark energy is the next frontier, and the CMB is the prime probe for it.

Remember “many diverse physics give wde(z)~-1.” For example, exponential f(R) gravity, barotopic fluids, DBI action all naturally give wobs~-1 despite totally different origins. To learn the physics, we must delve into the microphysics.

We are basically asking whether there are more degrees of freedom than in quintessence.

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OutlineOutline

1. Handles on Dark Energy

2. CMB Lensing and CMB-Galaxy Correlations

3. Early, Cold, and Stressed Dark Energy

4. Testing GR with the CMB

5. Is Acceleration Unique?

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CMB as a ProbeCMB as a Probe

CMB probes perturbations – that’s what the anisotropy power spectrum is, the spatial distribution of photons.

The photons undergo oscillations due to (EM) coupling to matter, forced/damped by gravity, and redshifted by gravity.

Dark energy perturbations contribute to the gravitational potential and affect the CMB.

W. Hu

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CMB as a ProbeCMB as a Probe

Dark energy microphysics enters in the Sachs-Wolfe effect on acoustic peak heights of T, E, TE spectra, in addition to the ISW and peak locations due to DE effects on expansion.

ISW(late time)

Sachs-Wolfe(recombination)

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CMB LensingCMB Lensing

Gravitational potentials (spatial variation) between recombination and the present also affect CMB through gravitational lensing.

This shifts and recorrelates the CMB (Linder 1988; older

than galaxy weak lensing (Linder 1990)!).

Main effects are smearing out peaks and generating B-mode polarization (from E-mode). [160μK 8μK 0.3μK]

Individual deflection ~ 4ψ ~ 10-4 ~ 20 Line of sight deflection ~ (H0

-1/L)1/2 × 20 ~ 2.5 Coherence scale ~ (L/H0

-1) ~ 2°

Want to extract lensing deflection field ψ on sky (OQE Hu 2001, Hu & Okamoto 2002).

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CMB – Galaxy CrosscorrelationCMB – Galaxy Crosscorrelation

Since the CMB photon perturbations and matter density perturbations were once tightly coupled, there’s correlation between hot/cold and void/dense.

These Tg correlations will be a powerful addition to pure CMB (cf. ISW), especially with nearly fully sky galaxy surveys.

Such correlations can also probe specific redshift slices.

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OutlineOutline

1. Handles on Dark Energy

2. CMB Lensing and CMB-Galaxy Correlations

3. Early, Cold, and Stressed Dark Energy

4. Testing GR with the CMB

5. Is Acceleration Unique?

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Early Dark EnergyEarly Dark Energy

When w~-1 then perturbations have no effect. We know today w~-1, plus perturbations today would only affect large scales (small l in the CMB).

So we need DE at high redshift, either z~1-5 for CMB lensing or Tg, or recombination for CMB itself.

Many such Early Dark Energy models exist, and indeed are quite common from high energy physics (dilaton, DBI, moduli, barotropic models).

Thus, there is a high redshift frontier for DE, that only CMB can explore.

Current constraints have ΩEDE<0.035 (95% cl de Putter,

Huterer, Linder 2010) but can still give important effects.[Ωb]

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Early, Cold, Stressed Dark EnergyEarly, Cold, Stressed Dark Energy

Early DE density parametrized by Doran & Robbers 2006 form. (Note ΩΛ(z=103)~10-9.)

Perturbations by sound speed cs2=dp/dρ.

Quintessence has cs2=1. Largest effect for smallest

cs2 – “cold dark energy”.

Finally, anisotropic stress cvis≠0 (Hu 1998).

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The Speed of DarkThe Speed of Dark

Current constraints on cs using CMB (WMAP5), CMB × gal (2MASS,SDSS,NVSS), gal (SDSS).

Best fit Ωe=0.02, cs=0.04, w0=-0.95 but consistent with Λ within 68% cl.

de Putter, Huterer, Linder 2010

★ ★

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CMB Lensing in the FutureCMB Lensing in the Future

CMB lensing adds powerful leverage on fundamental physics. Neutrino masses smooth perturbations through free streaming. Determining Σm < 0.1 eV decides normal vs. inverted hierarchy.

de Putter, Zahn, Linder 2009 de Putter 2009

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CMB Lensing in the FutureCMB Lensing in the Future

Must include full set of effects on matter power spectrum, e.g. neutrino mass, dark energy.

de Putter, Zahn, Linder 2009

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Early, Cold, Stressed Dark EnergyEarly, Cold, Stressed Dark Energy

Perturbations enhanced by lowering sound speed cs

2 (from 1) and suppressed by raising stress cvis

2 (from 0).

Enhanced perturbations strengthen gravitational potential, so reduce photon Sachs-Wolfe power and enhance ISW.

cs2

cvis2

Calabrese, de Putter, Huterer, Linder, Melchiorri 2010

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Early, Cold, Stressed Dark EnergyEarly, Cold, Stressed Dark Energy

Also affects CMB lensing. Enhanced perturbations

New degrees of freedom can be detected; testing consistency difficult.

Does not degrade other parameters.

★ ★

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OutlineOutline

1. Handles on Dark Energy

2. CMB Lensing and CMB-Galaxy Correlations

3. Early, Cold, and Stressed Dark Energy

4. Testing GR with the CMB

5. Is Acceleration Unique?

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Testing GravityTesting Gravity

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.

Can also test gravity in model-independent way.

Gravity and growth:

Gravity and acceleration:

Are and the same? (yes, in GR)

Daniel & Linder 2010 ; also Song 2010

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Current Data Testing GRCurrent Data Testing GR

Model independent test of GR: divide G, V into high/low z and high/low k bins – test time and scale dependence.

WMAP7+Union2+CFHTLS

WMAP7+Union2+CFHTLS+Tg+ggCOSMOS

“2x2x2 gravity”

Daniel & Linder 2010

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Future Data Testing GRFuture Data Testing GR

3D galaxy survey can play big role. Future data offer 5-10% tests of 8 post-GR parameters.

Dotted=Current

(TT+SN)space

+Tg+gg

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Nearer FutureNearer Future

σ8

Ωνh2Das & de Putter, in prep ; also see HSLS 1007.3519

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OutlineOutline

1. Handles on Dark Energy

2. CMB Lensing and CMB-Galaxy Correlations

3. Early, Cold, and Stressed Dark Energy

4. Testing GR with the CMB

5. Is Acceleration Unique?

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Testing Expansion HistoryTesting Expansion History

How well do we really know the standard picture of radiation domination matter domination dark energy domination?

Not well at all in detail. Although we know the magnitude of H, we don’t know its slope. Even during BBN, w=[0,1].

Maybe acceleration is occasional; two ways to get early acceleration:

Superacceleration Superdeceleration

w<<-1

w=+1

Carroll & Kaplinghat 2002

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Early AccelerationEarly Acceleration

Superacceleration: Less than 0.035 e-folds allowed by dynamics (if w too negative, Ωw driven too small to allow wtot<-1/3). Also, Nacc~(1+zacc)-3. Linder 2010

Superdeceleration: Best probe to early universe is CMB. Expansion enters in many ways!

We can probe back to when a mode entered the horizon: l >η0/η(zmod)

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CMB Probes of AccelerationCMB Probes of Acceleration

Post-recombination, peaks left and adds ISW. Pre-recombination, peaks right and adds SW.

Effect of 0.1 e-fold of accelerationLinder & Smith 2010

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Cosmic AccelerationCosmic Acceleration

WMAP7+ACT rules out extra acceleration back to z~3×104. Planck can test back to z~2×105.

Current acceleration unique within last factor 100,000 of cosmic expansion!

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SummarySummary

Spatial variation of dark energy and early dark energy are exciting frontiers, and the CMB is the prime probe for them.

CMB lensing and CMB-galaxy correlations can probe fundamental physics – neutrino mass, dark energy microphysics, gravity. E.g. “early, cold, or stressed” dark energy and 8 post-GR parameters to 10%.

Expansion history can be tested to z~105. Current acceleration appears unique!

“World Class University” program in Seoul, Korea. 8 postdocs hired, 5 more open, 2 new faculty open.