Dark energy and the CMB

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Dark energy and the CMB

• Robert Crittenden

Work with S. Boughn, T. Giannantonio, L.
Pogosian, N. Turok, R. Nichol, P.S. Corasaniti,
C. Stephan-Otto
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Why use the CMB to study dark energy?

• Naively, dark energy is a late universe effect,
  while the CMB primarily probes the physics of the
  last scattering surface.
• Extrapolating backwards, the expected energy
  density of baryons/dark matter is a billion times
  higher at z1000, while the dark energy density
  is about the same.
• Thus, we might not expect dark energy would much
  of an effect on the CMB!
• But despite this, it is a very useful tool in DE
  studies

Matter density
Dark energy
Radiation density
z1000
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Ways the CMB is useful for DE

• Provides an inventory of virtually everything
  else in the Universe, particularly what is
  missing!
• Acts as a standard ruler on the surface of last
  scattering with which we can measure the geometry
  of the Universe.
• Some CMB anisotropies are created very recently
• Integrated Sachs-Wolfe effect
• Non-linear effects like Sunyaev-Zeldovich
• In some dark energy models, like tracking models,
  the dark energy density can change significantly,
  so that it is important at z1000.

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CMB as cosmic yardstick
The CMB is imprinted with the scale of the sound
horizon at last scattering. Both the curvature
and the dark energy can change the angular size
of the Doppler peaks. Assuming a cosmological
constant, we get a constraint on
curvature. However, if we assume a flat universe,
we can find a constraint on the equation of
state.
WMAP compilation
Angular distance to last scattering surface
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Ways the CMB is useful for DE

• Provides an inventory of virtually everything
  else in the Universe.
• Acts as a standard ruler on the surface of last
  scattering with which we can measure the geometry
  of the Universe.
• Some CMB anisotropies are created very recently
• Integrated Sachs-Wolfe (ISW) effect
• Non-linear effects like Sunyaev-Zeldovich
• In some dark energy models, like tracking models,
  the dark energy density can change significantly,
  so that it is important at z1000.

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Outline

• What is the ISW effect?
• Why is it interesting?
• Detecting the ISW
• Examples
• X-ray background
• SDSS quasars
• Present limits
• Future measurements
• Improving the detections
• Conclusions

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Two independent CMB maps
The CMB fluctuations we see are a combination of
two largely uncorrelated pieces, one induced at
low redshifts by a late time transition in the
total equation of state.
Late ISW map, zlt 4 Mostly large scale features
Requires dark energy/curvature
Early map, z1000 Structure on many scales Sound
horizon as yardstick
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Dark energy signature

• The ISW effect is gravitational, much like
  gravitational lensing, but instead of probing the
  gravitational potential directly, it measures its
  time dependence along the line of sight.

potential depth changes as cmb photons pass
through
gravitational potential traced by galaxy density
The gravitational potential is actually constant
in a matter dominated universe on large scales.
However, when the equation of state changes, so
does the potential, and temperature anisotropies
are created.
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What can the ISW do for us?

• Differential measurement of structure evolution
• Only arises when matter domination ends!
• Independent evidence for dark energy
• Matter dominated universe in trouble
• Direct probe of the evolution of structures
• Do the gravitational potentials grow or decay?
• Constrain modified gravity models?
• Structure formation on the largest scales
• Measure dark energy clustering
• (Bean Dore, Weller Lewis, Hu Scranton)

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Modified gravity
Modified gravity theories might have very
different structure growth. Thus, they lead to
very different predictions for ISW even with the
same background expansion! Extra dimensional
changes typically affect largest scales the most.
This is where the predictions are most uncertain.
Lue, Scoccimarro, Starkman 03
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DGP model
On small scales, there is an anzatz (Koyama
Maartens) for solving for the growth of
structure, but things are still uncertain for
large scales. In the ISW, this leads to different
predictions, particularly at high redshifts where
a higher signal could be generated. The signal
at low l (l lt 20) is still uncertain, though a
new anzatz has recently been proposed. (Song,
Sawicki Hu).
Song, Sawicki Hu 06
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What can the ISW do for us?

• Differential measurement of structure evolution
• Only arises when matter domination ends!
• Independent evidence for dark energy
• Matter dominated universe in trouble
• Direct probe of the evolution of structures
• Do the gravitational potentials grow or decay?
• Constrain modified gravity models?
• Structure formation on the largest scales
• Measure dark energy clustering
• Potentially discriminate d.e. sound speeds at
  3?
• (Bean Dore, Weller Lewis, Hu Scranton)

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How do we detect ISW map?

• The typical scale is the horizon size, because
  smaller structures tend to cancel out.
• On linear scales positive and negative effects
  equally likely.
• Difficult to measure directly
• Same frequency dependence.
• Small change to spectrum.
• Biggest just where cosmic variance is largest.
• But we can see it if we look for correlations of
  the CMB with nearby (z lt 2) matter!

RC N. Turok 96 SDSS H. Peiris D. Spergel
2000
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Cross correlation spectrum
The gravitational potential determines where the
galaxies form and where the ISW fluctuations are
created! Thus the galaxies and the CMB should be
correlated, though its not a direct
template. Most of the cross correlation arises on
large or intermediate angular scales (gt1degree).
The CMB is well determined on these scales by
WMAP, but we need large galaxy surveys.
Can we observe this? Yes, but its difficult!
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Fundamental problem
While we see the CMB very well, the usual signal
becomes a contaminant when looking for the
recently created signal. Effectively we are
intrinsically noise dominated and the only
solution is to go for bigger area. But we are
fundamentally limited by having a single sky.
Noise!
Signal
ISW map, zlt 4
Early map, z1000
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Example hard X-ray background

• XRB dominated by AGN at z 1.
• Remove possible contaminants from both
• Galactic plane, center
• Brightest point sources
• Fit monopole, dipole
• Detector time drifts
• Local supercluster

Hard X-ray background - HEAO-1
CMB sky - WMAP
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Cross correlations observed!
dots observed thin Monte Carlos thick ISW
prediction given best cosmology and dN/dz errors
highly correlated
S. Boughn RC, 2004

• What is the significance?
• Dominated not by measurement errors, but by
  possible accidental alignments.
• This is modeled by correlating the XRB with
  random CMB maps with the same spectrum.
• This gives the covariance matrix for the various
  bins.
• Result 3 ??detection

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Could it be a foreground?

• Possible contaminations
• Galactic foregrounds
• Clustered extra-galactic sources emitting in
  microwave
• Sunyaev-Zeldovich effect
• Tests
• insensitive to level of galactic cuts
• insensitive to point source cuts
• comparable signal in both hemispheres
• correlation on large angular scales
• independent of CMB frequency channel

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CMB frequency independence
Cross correlations for ILC and various WMAP
frequency bands lie on top of each other. Not
the strong dependence expected for sources
emitting in the microwave.
Radio-WMAP
XRB-WMAP
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A few contaminated pixels?
The contribution to the correlation from
individual pixels pairs is consistent with what
is expected for a weak correlation. Correlation
is independent of threshold, thus NOT dominated
by a few pixels blue product of two
Gaussians red product of two weakly correlated
Gaussians
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Highest redshift detection of ISW

• To understand the evolution of the potential, its
  important to push to higher redshifts.
• One possible sample is the SDSS quasars (Peiris
  Spergel 2000).
• We use the photometrically selected sample of
  Richards et al. 2004
• 300,000 objects up to z 2.7.
• Covers 16 of the sky.
• Some fraction (5) are local stars that are hard
  to distinguish in color space.
• Highest mean redshift of all ISW studies so far
  objects have individual redshifts!

T. Giannantonio, RC, R. Nichol et al -
astro-ph/0607572
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QSO map

• We pixelize using HEALPIX, same as WMAP data.
• We correct those edge pixels which are partially
  within the SDSS mask, weighting them less.
• We explore the effects of potential systematics
• Dust extinction
• Poor seeing
• Bright sources
• Sky brightness
• The largest effect is the extinction, so we cut
  out the 20 most reddened pixels.

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QSO ACF

• We first calculate the QSO ACF on large scales.
• The amplitude of correlations and inferred bias
  are consistent with earlier measurements (Myers
  et al.)
• A significant correlation is seen on large
  angles, in excess of what is expected from
  theory.
• This is consistent with the 5 contamination from
  stars, and provides a useful cross check.

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QSO-WMAPII CCF

• The correlation with WMAP ILC is seen at roughly
  the expected level and angular dependence.
• Significance level 2.0-2.5 ?, depending on masks,
  etc. A 0.31 - 0.14
• Seen to be independent of CMB frequency.
• Error bars calculated with 2000 Monte Carlo
  simulations.
• Q map has small residual correlations with stars,
  but this does not seem to affect its correlation
  with the QSO sample.
• With full SDSS sample, we will break this up into
  different redshift slices.

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Correlations seen in many frequencies!

• X-ray background (Boughn RC)
• SDSS quasars (Giannantonio, RC, et al.)
• Radio galaxies
• NVSS confirmed by Nolta et al (WMAP
  collaboration)
• Wavelet analysis shows even higher significance
  (Vielva et al. McEwan et al.)
• FIRST radio galaxy survey (Boughn)
• Infrared galaxies
• 2MASS near infrared survey (Afshordi et al.)
• Optical galaxies
• APM survey (Folsalba Gaztanaga)
• Sloan Digital Sky Survey (Scranton et al., FGC,
  Cabre et al.)
• Band power analysis of SDSS data (N. Pamanabhan,
  et al.)

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Detections of ISW

• Correlations seen at many frequencies, covering a
  wide range in redshift.
• All consistent with cosmological constant model,
  if a bit higher than expected. This has made them
  easier to detect!
• Relatively weak detections, and there is
  covariance between different observations!
• Correlations shown at 6 degrees to avoid
  potential small angle contaminations (e.g. SZ).
  (Gaztanga et al.)

APM
SDSS
2mass
X-ray/NVSS
New!
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Scale with comoving distance
APM
SDSS
2mass
X-ray/NVSS
QSO
Signal declines and moves to smaller scales at
higher redshift.
We plot the observations for a fixed projected
distance.
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What does it say about DE?

• Thus far constraints are fairly weak from ISW
  alone.
• Consistent with cosmological constant model.
• Can rule out models with much larger or negative
  correlations.
• Very weak constraints on DE sound speed.

Corasantini, Giannantonio, Melchiorri
05 Gaztanaga, Manera, Multamaki 04
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Parameter constraints

• A more careful job is needed!
• Quantify uncertainties
• Bias - usually estimated from ACF consistently.
  How much does it evolve over the samples?
  Non-linear or wavelength dependent?
• Foregrounds - incorporate them into errors.
• dN/dz - how great are the uncertainties?
• Understand errors
• To use full angular correlations, we need full
  covariances for all cross correlations.
• Monte Carlos needed with full cross correlations
  between various surveys.

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Extended covariance matrix

• To combine them, we must understand whether and
  how the various experiments could be correlated
• Overlaps in sky coverage and redshift.
• Magnification bias.
• First efforts have begun to combine (Ryan
  Scranton TG)
• NVSS
• SDSS, LRG QSO
• 2MASS
• Preliminary results indicate gt 5? total signal!

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How good will it get?
For the favoured cosmological constant the best
signal to noise one can expect is about 7-10.
This requires significant sky coverage, surveys
with large numbers of galaxies and some
understanding of the bias. The contribution to
(S/N)2 as a function of multipole moment. This
is proportional to the number of modes, or the
fraction of sky covered, though this does depend
on the geometry somewhat. Of course, this
assumes we have the right model-- It might be
more!
RC, N. Turok 96 Afshordi 2004
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Future forecasts

• Ideal experiment
• Full sky, to overcome noise
• 3-D survey, to weight in redshift (photo-z ok)
• z 2-3, to see where DE starts
• 107 -108 galaxies, to beat Poisson noise
• Unfortunately, z1000 noise limits the signal
  to the 7-10? level, even under the best
  conditions.
• Realistic plans
• Short term - DES, Astro-F (AKARI)
• Long term - LSST, LOFAR/SKA

Pogosian et al 2005 astro-ph/ 0506396
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Getting rid of the noise
Is there any way to eliminate the noise from the
intrinsic CMB fluctuations? Suggestion from L.
Page use polarization!
The CMB is polarized, and this occurs before ISW
arises, either at recombination or very soon
after reionization! Can we use this to subtract
off the noise? To some extent, yes!
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The polarized temperature map
Suppose we had a good full sky polarization map
(EE) and a theory for the cross correlation (TE).
We could use this to estimate a temperature map
(e.g. Jaffe 03) that was 100 correlated with
the polarization. Subtracting this from the
observed map would reduce the noise somewhat,
improving the ISW detection! Only a small
effect at the multipoles relevant for the ISW,
but could improve S/N by 20.
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Wavelet detections

• Recent wavelet analyses (Vielva et al., McEwen et
  al) have apparently claimed better significance
  of detections than analyses using correlation
  functions.
• NVSS-WMAP
• CCFs give 2-2.5 ??ISW detections.
• Wavelets give 3.3-3.9 ? correlation detections.
• Despite better detection, parameter constraints
  comparable?!
• Whats going on?
• Claims
• Wavelets localize regions that correlate most
  strongly.
• Better optimized for a single statistic than
  CCF(0).

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Wavelet method

• Wavelet analysis
• Modulate both maps with wavelet filter (e.g.
  SMH).
• Take the product of two new maps (effectively
  CCF(0).)
• Compare this to expected variance.
• Repeat for different sizes, shapes, orientations
  largest is reported as detection significance.
• Use all wavelets and covariances for parameter
  constraints.
• The quoted wavelet detection significances are
  biased! It does not try to match what is seen
  from what is theoretically expected. They
  actually present the probability of measuring
  precisely what they saw. The more wavelets they
  try, the better the more significant the
  detections will appear.

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Wavelets vs correlation functions
Assuming the maps are Gaussian, the CCF or the
power spectrum should be sufficient they should
contain all the information in the
correlations. It is true that wavelets do better
for a single statistic, but CCF measurements look
for particular angular dependence, combining
different bins with full covariance. In both
cases, Gaussianity of quadratic statistics is
assumed. The true full covariance distribution
should be calculated to get true significance.
Wavelets could be improved by using information
about the expected ISW signal, and the optimal
wavelet is simple to calculate, but it is not
compact.
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Conclusions

• ISW effect is a useful cosmological probe,
  capable of telling us useful information about
  nature of dark energy.
• It has been detected in a number of frequencies
  and a range of redshifts, providing independent
  confirmation of dark energy.
• Many measurements are higher than expected, but
  what is the significance?
• There is still much to do
• Fully understanding uncertainties and covariances
  to do best parameter estimation.
• Using full shape of probability distributions.
• Finding new data sets.
• Reducing noise with polarization information.