Constraints on Dark Energy from CMB

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Constraints on Dark Energy from CMB

• Eiichiro Komatsu
• University of Texas at Austin
• Dark Energy Meeting_at_Ringberg
• February 27, 2006

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Can CMB Constrain the Nature of Dark Energy?

• Which DE?
• Early Dark Energy (Inflaton Field)
• Intermediate Dark Energy (Tracker Field)
• Late Dark Energy
• Prospects for constraining the nature of DE with
  CMB ONLY is
• Not so good for Early DE, if B-mode pol. is not
  detected.
• Not so good for Intermediate DE
• Not so good for Late DE
• Combination of CMB, LSS SN is very powerful for
  constraining all of them (and everyone knows
  that), but let me try to talk just about CMB for
  45 minutes (not so easy these days).

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What Can CMB Measure?

• Baryon-to-photon ratio
• Sound speed and inertia of baryon-photon fluid
• Matter-to-radiation ratio
• Matter-radiation equality
• Radiation may include photons, neutrinos as
  well as any other relativistic components.
• Angular diameter distance to decoupling surface
• Peak position in l space (Sound
  horizon)/(Angular Diameter Distance)
• Time dependence of gravitational potential
• Integrated Sachs-Wolfe Effect
• Primordial power spectrum (ScalarTensor)
• Optical depth

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What CMB Measures
Amplitude of temperature fluctuations at a given
scale, lp/q
400
800
200
40
100
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Multipole moment lp/q
Small scales
Large scales
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CMB to Parameters
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Matter-Radiation Ratio

• More extra radiation component means that the
  equality happens later.
• Since gravitational potential decays during the
  radiation era (free-fall time scale is longer
  than the expansion time scale during the
  radiation era), ISW effect increases anisotropy
  at around the Horizon size at the equality.

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Matter, n, or Q?
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Angular Diameter Distance
dAconstant
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Error in dA Error in rs
rs
dA
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ISW Effect
Therefore, one might hope that the ISW would help
to break degeneracy between w and the other
parameters. However
w-2
w-0.6
Weller Lewis (2003)
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Perturbations in DE

• Dark energy is required to be uniform in space
  (I.e., no fluctuations) if it is a cosmological
  constant (w-1).
• However, in general dark energy can fluctuate and
  cluster on large scales when w is not -1.
• The clustering of DE can
• source the growth of potential,
• compensate the suppression of growth due to a
  faster expansion rate, and
• lower the ISW effect.

• This property makes it absolutely impossible to
  constraint w with CMB alone, no matter how good
  the CMB data would be.

Weller Lewis (2003)
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CMB-LSS Correlation

• The same gravitational potential would cause ISW
  and LSS. Cross-correlation signal is an important
  cross-check of the existence of dark energy.
  There are 2-sigma detections of various
  correlations
• Boughn and Crittenden (2004) WMAP x Radio
  X-ray sources
• Nolta et al. (2004) WMAP x NVSS radio sources
• Scranton et al. (2003) WMAP x LRGs in SDSS
• Afshordi et al. (2004) WMAP x 2MASS galaxies
• But its hard!
• CMB is already signal-dominated on large scales,
  so nothing to be improved on the CMB side.
• An all-sky galaxy survey observing 10 million
  galaxies at 0ltzlt1 gives only 5-sigma detection
  (Afshordi 2004).

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CMB-WL Correlation
RS

• Non-linear growth of structure at small scales
  also provides the ISW signal (a.k.a. RS effect)
• Would that be observable (ever)?
• The future lensing experiments would be
  signal-dominated.
• A lot of room for CMB experiments to improve at
  small scales.

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• The RS-WL correlation picks up a time-derivative
  of the growth rate of structure a sensitive
  measure of w
• Several different source redshifts allow us to do
  tomography on the time derivatives.

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RS-WL Correlation Prediction
Nishizawa Komatsu (in prep.)
Assumed CMB experiment 100deg2, 1 arcmin
resolution, 1uK noise per pixel
Positive Correlation (ISW)
High S/N!
Negative Correlation (RS)
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Summary

• CMB constraints DE properties via
• Matter-to-radiation Ratio (useful for
  constraining Tracker field)
• Angular Diameter Distance (degeneracy lines in
  w-h and w-Omega)
• ISW (not very useful)
• Massive degeneracy between w and h and matter
  density makes it absolutely impossible for CMB
  alone to constrain DE properties.
• It does not matter how good the CMB data would
  be.
• It is essential to combine it with LSS and/or
  SNe.
• CMB-WL correlation may serve as an additional
  test of DE properties.
• Future small-scale CMB experiments might want to
  increase their angular resolution to 1 arcmin
  level.

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