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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
Measurements of CMB anisotropies
 Beautiful new data from
WMAP and smaller angle
experiments
 What do they tell us about
dark energy?
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 z=1000, 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
densit
y
Dark
energ
y
z=1000
Last scattering
Radiatio
n density
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 z=1000.
What might we learn about DE?
 How much of it is there?
 Parameterized in terms of its present density
 How does it evolve?
 What is its equation of state?
 How does it cluster?
 Smooth on small scales, but might cluster on large scales
 Characterized by the DE sound horizon,
 Is it really matter or is it modified gravity?
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 z=1000.
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Dark energy density we’re trying to determine
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Photon density constraint (0.004 %):
• Observed CMB temperature
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Total matter density (dark matter + baryons):
• CMB Doppler peak heights
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Baryon density constraints:
• Light element abundances
• CMB Doppler peak ratios
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Neutrino density constraints (< 1%):
• Small scale damping in LSS
• Overall neutrino mass limits
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Curvature of universe constraint (< 2%):
• Angular size of CMB structures
• Limit depends on dark energy assumptions
Weighing the universe
There must be enough matter to explain the
present expansion rate:
Critical density constraint:
• Measurement of Hubble constant
• Biggest source of possible systematic errors
Weighing the universe
Bottom line:
Much of the uncertainty comes
from the late Universe, so an
improvement in the Hubble
constant measurement would
be very useful!
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 z=1000.
CMB as cosmic yardstick
Physical size of acoustic sound horizon
The time of recombination
and the sound speed are
well determined, telling us
what this important scale is.
CMB as cosmic yardstick
Angular distance to last scattering surface
CMB as cosmic yardstick
If we have a small amount of curvature,
this will change the observed angular size.
This is very hard to distinguish from
changes to the angular distance to the last
scattering.
WMAP figure
CMB as cosmic yardstick
The CMB is imprinted with the
scale of the sound horizon at last
scattering. This characteristic
scale is shown by the Doppler
peaks.
WMAP compilation
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 dark energy density and
its evolution.
Fix angular scale of sound horizon
CMB as cosmic yardstick
WMAP3 results
The CMB fixes a single integrated quantity and
has a fundamental degeneracy between the
dark energy density and its equation of state,
which can be broken by other observations.
Even including all the other data, a
degeneracy remains between the
equation of state and a small
amount of curvature.
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 z=1000.
ISW overview
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
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.
Early map, z~1000
Structure on many
scales Sound horizon as
Late ISW map, z< 4
Mostly large scale features
Requires dark energy/curvature
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.
gravitational potential
traced by galaxy density
potential depth
changes as cmb
photons pass
through
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.
What can the ISW do for us?
Independent evidence for dark energy
 Shows how DE affects growth of perturbations
 Matter dominated universe in trouble
Differential measurement of structure evolution
 Only arises when matter domination ends!
Direct probe of the evolution of structures
 Do the gravitational potentials grow or decay?
 Constrain modified gravity models?
Probes structure formation on the largest scales
 Measure dark energy clustering
(Bean & Dore, Weller & Lewis, Hu & Scranton)
What can the ISW do for us?
Independent evidence for dark energy
 Shows how DE affects growth of perturbations
 Matter dominated universe in trouble
Differential measurement of structure evolution
 Only arises when matter domination ends!
Direct probe of the evolution of structures
 Do the gravitational potentials grow or decay?
 Constrain modified gravity models?
Probes structure formation on the largest scales
 Measure dark energy clustering
(Bean & Dore, Weller & Lewis, Hu & Scranton)
What can the ISW do for us?
Independent evidence for dark energy
 Shows how DE affects growth of perturbations
 Matter dominated universe in trouble
Differential measurement of structure evolution
 Only arises when matter domination ends!
Direct probe of the evolution of structures
 Do the gravitational potentials grow or decay?
 Constrain modified gravity models?
Probes structure formation on the largest scales
 Measure dark energy clustering
(Bean & Dore, Weller & Lewis, Hu & Scranton)
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
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 < 20) is
still uncertain, though a new
anzatz has recently been
proposed. (Song, Sawicki &
Hu).
Song, Sawicki & Hu 06
What can the ISW do for us?
Independent evidence for dark energy
 Shows how DE affects growth of perturbations
 Matter dominated universe in trouble
Differential measurement of structure evolution
 Only arises when matter domination ends!
Direct probe of the evolution of structures
 Do the gravitational potentials grow or decay?
 Constrain modified gravity models?
Probes structure formation on the largest scales
 Measure dark energy clustering on horizon scale
(Bean & Dore, Weller & Lewis, Hu & Scranton)
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 < 2) matter!
RC & N. Turok 96
SDSS: H. Peiris & D. Spergel 2000
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 (>1degree). The
CMB is well determined on
these scales by WMAP, but we
need large galaxy surveys.
Can we observe this? Yes, but its difficult!
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.
Signal
ISW map, z< 4
Noise
!
Early map, z~1000
Example: hard X-ray background
XRB dominated by AGN
at z ~ 1.
Remove possible
contaminants from both:
Hard X-ray background - HEAO-1
 Galactic plane, center
 Brightest point sources
 Fit monopole, dipole
 Detector time drifts
 Local supercluster
CMB sky - WMAP
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
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
• comparable signal in both hemispheres
• insensitive to point source cuts
• correlation on large angular scales
• independent of CMB frequency channel
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.
XRBWMAP
Radio-WMAP
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
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
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.
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.
Stellar contamination?
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.
Highly correlated errors!
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.)
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.)
2mass
APM
SDSS

Xray/NVSS
New!
Scale with comoving distance
AP
2mass M
SDSS
Xray/NVSS
QSO
Signal declines and moves to
smaller scales at higher redshift.
We plot the observations for a
fixed projected distance.
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
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 Carlo’s needed with full cross correlations
between various surveys.
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 > 5
total signal!
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
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, z=1000 ‘noise’ limits the signal to the 7-10
level, even under the best conditions.
Realistic plans:
 Short term - DES, Astro-F (AKARI)
Pogosian et al
 Long term - LSST, LOFAR/SKA
2005
astro-ph/ 0506396
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!
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%.
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?!
What’s going on?
Claims:
 Wavelets localize regions that correlate most strongly.
 Better optimized for a single statistic than CCF(0).
Wavelet method
Wavelet analysis:
1. Modulate both maps with wavelet filter (e.g. SMH).
2. Take the product of two new maps (effectively CCF(0).)
3. Compare this to expected variance.
4. Repeat for different sizes, shapes, orientations; largest is
reported as detection significance.
5. 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.
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.
Conclusions
Despite primarily originating in the early Universe, CMB anisotropies
have told us much about dark energy, constraining both its density
and its evolution.
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.
Rees-Sciama
Integration through
Millennium simulation
including ISW and the
Rees-Sciama effect
from clusters.
Volker Springel, MPA
An important foreground
for the R-S effect is the
thermal SZ effect.