498 research outputs found
Cosmology with Weak Lensing Surveys
Weak gravitational lensing surveys measure the distortion of the image of
distant sources due to the deflections of light rays by the fluctuations of the
gravitational potential along the line of sight. Since they probe the
non-linear matter power spectrum itself at medium redshift such surveys are
complimentary to both galaxy surveys (which follow stellar light) and cosmic
microwave background observations (which probe the linear regime at high
redshift). Ongoing CMB experiments such as WMAP and the future Planck satellite
mission will measure the standard cosmological parameters with unprecedented
accuracy. The focus of attention will then shift to understanding the nature of
dark matter and vacuum energy: several recent studies suggest that lensing is
the best method for constraining the dark energy equation of state. During the
next 5 year period ongoing and future weak lensing surveys such as the Joint
Dark Energy Mission (JDEM, e.g. SNAP) or the Large-aperture Synoptic Survey
Telescope (LSST) will play a major role in advancing our understanding of the
universe in this direction. In this review article we describe various aspects
of weak lensing surveys and how they can help us in understanding our universe.Comment: 15 pages, review article to appear in 2005 Triennial Issue of Phil.
Trans.
Detectability of CMB tensor B modes via delensing with weak lensing galaxy surveys
We analyze the possibility of delensing CMB polarization maps using
foreground weak lensing (WL) information. We build an estimator of the CMB
lensing potential out of optimally combined projected potential estimators to
different source redshift bins. Our estimator is most sensitive to the redshift
depth of the WL survey, less so to the shape noise level. Estimators built
using galaxy surveys like LSST and SNAP yield a 30-50% reduction in the lensing
B-mode power. We illustrate the potential advantages of a 21-cm survey by
considering a fiducial WL survey for which we take the redshift depth zmax and
the effective angular concentration of sources n as free parameters. For a
noise level of 1 muK arcmin in the polarization map itself, as projected for a
CMBPol experiment, and a beam with FWHM=10 arcmin, we find that going to
zmax=20 at n=100 gal/sqarcmin yields a delensing performance similar to that of
a quadratic lensing potential estimator applied to small-scale CMB maps: the
lensing B-mode contamination is reduced by almost an order of magnitude. In
this case, there is also a reduction by a factor of ~4 in the detectability
threshold of the tensor B-mode power. At this CMB noise level, there is little
gain from sources with zmax>20. The delensing gains are lost if the CMB beam
exceeds ~20 arcmin. The delensing efficiency and useful zmax depend acutely on
the CMB map noise level, but beam sizes below 10 arcmin do not help. Delensing
via foreground sources does not require arcminute-resolution CMB observations,
a substantial practical advantage over the use of CMB observables for
delensing.Comment: 10 pages, 5 figures; accepted for publication in Physical Review
Lensing effect on the relative orientation between the Cosmic Microwave Background ellipticities and the distant galaxies
The low redshift structures of the Universe act as lenses in a similar way on
the Cosmic Microwave Background light and on the distant galaxies (say at
redshift about unity). As a consequence, the CMB temperature distortions are
expected to be statistically correlated with the galaxy shear, exhibiting a
non-uniform distribution of the relative angle between the CMB and the galactic
ellipticities. Investigating this effect we find that its amplitude is as high
as a 10% excess of alignement between CMB and the galactic ellipticities
relative to the uniform distribution. The relatively high signal-to-noise ratio
we found should makes possible a detection with the planned CMB data sets,
provided that a galaxy survey follow up can be done on a sufficiently large
area. It would provide a complementary bias-independent constraint on the
cosmological parameters.Comment: 7 pages, 3 figures; uses emulateapj.sty; submitted to Ap
The three-point correlation function of cosmic shear. II: Relation to the bispectrum of the projected mass density and generalized third-order aperture measures
We study the relation of the three-point cosmic shear statistics to the
third-order statistical properties of the underlying convergence, expressed in
terms of its bispectrum. Explicit relations for the natural components of the
shear three-point correlation function in terms of the bispectrum are derived.
The behavior of the correlation function under parity transformation is
obtained and found to agree with previous results. We find that in contrast to
the two-point shear correlation function, the three-point function at a given
angular scale \theta is not affected by power in the bispectrum on much larger
scales. These relations are then inverted to obtain the bispectrum in terms of
the three-point shear correlator; two different expressions, corresponding to
different natural components of the shear correlator, are obtained and can be
used to separate E and B-mode shear contributions. These relations allow us to
explicitly show that correlations containing an odd power of B-mode shear
vanish for parity-symmetric fields. Generalizing a recent result by Jarvis et
al., we derive expressions for the third-order aperture measures, employing
multiple angular scales, in terms of the (natural components of the)
three-point shear correlator and show that they contain essentially all the
information about the underlying bispectrum. We discuss the many useful
features these (generalized) aperture measures have that makes them convenient
for future analyses of the skewness of the cosmic shear field (and any other
polar field, such as the polarization of the Cosmic Microwave Background).
(Abridged)Comment: 18 pages, 3 figures, minor changes made, one paragraph and two
figures added. Matches the published versio
Nonlinearity and stochasticity in the density--velocity relation
We present results of the investigations of the statistical properties of a
joint density and velocity divergence probability distribution function (PDF)
in the mildly non-linear regime. For that purpose we use both perturbation
theory results, extended here for a top-hat filter, and numerical simulations.
In particular we derive the quantitative (complete as possible up to third
order terms) and qualitative predictions for constrained averages and
constrained dispersions -- which describe the nonlinearities and the
stochasticity properties beyond the linear regime -- and compare them against
numerical simulations. We find overall a good agreement for constrained
averages; however, the agreement for constrained dispersions is only
qualitative. Scaling relations for the Omega-dependence of these quantities are
satisfactory reproduced.
Guided by our analytical and numerical results, we finally construct a robust
phenomenological description of the joint PDF in a closed analytic form. The
good agreement of our formula with results of N-body simulations for a number
of cosmological parameters provides a sound validation of the presented
approach.
Our results provide a basis for a potentially powerful tool with which it is
possible to analyze galaxy survey data in order to test the gravitational
instability paradigm beyond the linear regime and put useful constraints on
cosmological parameters. In particular we show how the nonlinearity in the
density--velocity relation can be used to break the so-called Omega-bias
degeneracy in cosmic density-velocity comparisons.Comment: 12 pages, 11 figures; revised version with minor changes in the
presentation, accepted for publication in MNRA
Biased-estimations of the Variance and Skewness
Nonlinear combinations of direct observables are often used to estimate
quantities of theoretical interest. Without sufficient caution, this could lead
to biased estimations. An example of great interest is the skewness of
the galaxy distribution, defined as the ratio of the third moment \xibar_3
and the variance squared \xibar_2^2. Suppose one is given unbiased estimators
for \xibar_3 and \xibar_2^2 respectively, taking a ratio of the two does
not necessarily result in an unbiased estimator of . Exactly such an
estimation-bias affects most existing measurements of . Furthermore,
common estimators for \xibar_3 and \xibar_2 suffer also from this kind of
estimation-bias themselves: for \xibar_2, it is equivalent to what is
commonly known as the integral constraint. We present a unifying treatment
allowing all these estimation-biases to be calculated analytically. They are in
general negative, and decrease in significance as the survey volume increases,
for a given smoothing scale. We present a re-analysis of some existing
measurements of the variance and skewness and show that most of the well-known
systematic discrepancies between surveys with similar selection criteria, but
different sizes, can be attributed to the volume-dependent estimation-biases.
This affects the inference of the galaxy-bias(es) from these surveys. Our
methodology can be adapted to measurements of analogous quantities in quasar
spectra and weak-lensing maps. We suggest methods to reduce the above
estimation-biases, and point out other examples in LSS studies which might
suffer from the same type of a nonlinear-estimation-bias.Comment: 28 pages of text, 9 ps figures, submitted to Ap
The velocity-density relation in the spherical model
We study the cosmic velocity-density relation using the spherical collapse
model (SCM) as a proxy to non-linear dynamics. Although the dependence of this
relation on cosmological parameters is known to be weak, we retain the density
parameter Omega_m in SCM equations, in order to study the limit Omega_m -> 0.
We show that in this regime the considered relation is strictly linear, for
arbitrary values of the density contrast, on the contrary to some claims in the
literature. On the other hand, we confirm that for realistic values of Omega_m
the exact relation in the SCM is well approximated by the classic formula of
Bernardeau (1992), both for voids (delta<0) and for overdensities up to delta ~
3. Inspired by this fact, we find further analytic approximations to the
relation for the whole range delta from -1 to infinity. Our formula for voids
accounts for the weak Omega_m-dependence of their maximal rate of expansion,
which for Omega_m < 1 is slightly smaller that 3/2. For positive density
contrasts, we find a simple relation div v = 3 H_0 (Omega_m)^(0.6) [
(1+delta)^(1/6) - (1+delta)^(1/2) ], that works very well up to the turn-around
(i.e. up to delta ~ 13.5 for Omega_m = 0.25 and neglected Omega_Lambda). Having
the same second-order expansion as the formula of Bernardeau, it can be
regarded as an extension of the latter for higher density contrasts. Moreover,
it gives a better fit to results of cosmological numerical simulations.Comment: 11 pages, 6 figures. Accepted for publication in MNRA
Cosmological Information from Lensed CMB Power Spectra
Gravitational lensing distorts the cosmic microwave background (CMB)
temperature and polarization fields and encodes valuable information on
distances and growth rates at intermediate redshifts into the lensed power
spectra. The non-Gaussian bandpower covariance induced by the lenses is
negligible to l=2000 for all but the B polarization field where it increases
the net variance by up to a factor of 10 and favors an observing strategy with
3 times more area than if it were Gaussian. To quantify the cosmological
information, we introduce two lensing observables, characterizing nearly all of
the information, which simplify the study of non-Gaussian impact, parameter
degeneracies, dark energy models, and complementarity with other cosmological
probes. Information on the intermediate redshift parameters rapidly becomes
limited by constraints on the cold dark matter density and initial amplitude of
fluctuations as observations improve. Extraction of this information requires
deep polarization measurements on only 5-10% of the sky, and can improve Planck
lensing constraints by a factor of ~2-3 on any one of the parameters w_0, w_a,
Omega_K, sum(m_nu) with the others fixed. Sensitivity to the curvature and
neutrino mass are the highest due to the high redshift weight of CMB lensing
but degeneracies between the parameters must be broken externally.Comment: 19 pages, 16 figures, submitted to PR
Numerical Analyses of Weakly Nonlinear Velocity-Density Coupling
We study evolution of various statistical quantities of smoothed cosmic
density and velocity fields using N-body simulations. The parameter
characterizes nonlinear coupling of
these two fields and determines behavior of bulk velocity dispersion as a
function of local density contrast.
It is found that this parameter depends strongly on the smoothing scale even
in quasi-linear regimes where the skewness parameter
is nearly constant and close to the predicted value by the second-order
perturbation theory. We also analyze weakly nonlinear effects caused by an
adaptive smoothing known as the gather approach.Comment: 22 pages, 4 figures, to appear in ApJ (558, Sep 10
The Skewness of the Aperture Mass Statistic
We present simple formulae for calculating the skewness and kurtosis of the
aperture mass statistic for weak lensing surveys which is insensitive to
masking effects of survey geometry or variable survey depth. The calculation is
the higher order analog of the formula given by Schneider et al (2002) which
has been used to compute the variance of the aperture mass from several lensing
surveys. As our formula requires the three-point shear correlation function, we
also present an efficient tree-based algorithm for measuring it. We show how
our algorithm would scale in computing time and memory usage for future lensing
surveys. Finally, we apply the procedure to our CTIO survey data, originally
described in Jarvis et al (2003). We find that the skewness is positive
(inconsistent with zero) at the 2 sigma level. However, the signal is too noisy
from this data to usefully constrain cosmology.Comment: 16 pages, accepted by MNRAS. Minor revisions; this replacement
matches the accepted versio
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