Constraints on Dark Energy from CMB
Eiichiro Komatsu
University of Texas at Austin Dark Energy Meeting@Ringberg
February 27, 2006
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 constrai
ning all of them (and everyone knows that), but let me try to
talk just about CMB for 45 minutes (not so easy these days).
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 (Scalar+Tensor)
• Optical depth
What CMB Measures
mplitude of temperature fluctuations at a given scale, l
400 800
200 40 100
10
Multipole moment
l~
Small scales Large scalesAng.Diam. Distance
Baryon-to- photon
Ratio
Mat-to- Radiatio n Ratio
ISW
CMB to Parameters
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.Matter, , or Q?
Angular Diameter Distance
d
A=constant
Error in d A = Error in r s
A
r s
d A
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
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.
Weller & Lewis (2003)
•This property makes it
absolutely impossible to
constraint w with CMB
alone, no matter how
good the CMB data
would be.
CMB-LSS Correlation
• The same gravitational potential would cause ISW and L SS. Cross-correlation signal is an important cross-check of the existence of dark energy. There are ~2-sigma det ections of various correlations:
Boughn and Crittenden (2004): WMAP x Radio & X-ray source s
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 it’s 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 0<z<1 gives only 5-sigma detection (Afshordi 2004).
CMB-WL Correlation
• Non-linear growth of structure at small scales also provi des 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.
RS
• The RS-WL correlation picks up a time-derivative of the growth rat e of structure: a sensitive measure of w
• Several different source redshifts allow us to do tomography on th
e time derivatives.
RS-WL Correlation: Prediction
Nishizawa & Komatsu (in prep.)
Positive Correlation (ISW)
Negative Correlation (RS)
Assumed CMB experiment: 100deg
2, 1 arcmin resolution, 1uK noise per pixel
High S/N!
Summary
• CMB constraints DE properties via
Matter-to-radiation Ratio (useful for constraining Tracker fie ld)
Angular Diameter Distance (degeneracy lines in w-h and w -Omega)
ISW (not very useful)
• Massive degeneracy between w and h and matter de nsity makes it absolutely impossible for CMB alone t o 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.
