452 research outputs found
CMB Lensing Reconstruction in Real Space
We explore the reconstruction of the gravitational lensing field of the
cosmic microwave background in real space showing that very little statistical
information is lost when estimators of short range on the celestial sphere are
used in place of the customary estimators in harmonic space, which are nonlocal
and in principle require a simultaneous analysis of the entire sky without any
cuts or excisions. Because virtually all the information relevant to lensing
reconstruction lies on angular scales close to the resolution scale of the sky
map, the gravitational lensing dilatation and shear fields (which unlike the
deflection field or lensing potential are directly related to the observations
in a local manner) may be reconstructed by means of quadratic combinations
involving only very closely separated pixels. Even though harmonic space
provides a more natural context for understanding lensing reconstruction
theoretically, the real space methods developed here have the virtue of being
faster to implement and are likely to prove useful for analyzing realistic maps
containing a galactic cut and possibly numerous small excisions to exclude
point sources that cannot be reliably subtracted.Comment: 21 pages, 8 figure
The Fundamental Plane of Galaxy Clusters
Velocity dispersion , radius and luminosity of elliptical
galaxies are known to be related, leaving only two degrees of freedom and
defining the so-called ``fundamental plane". In this {\em Letter} we present
observational evidence that rich galaxy clusters exhibit a similar behaviour.
Assuming a relation , the best-fit values
of and are very close to those defined by galaxies. The
dispersion of this relation is lower than 10 percent, i.e. significantly
smaller than the dispersion observed in the and relations. We
briefly suggest some possible implications on the spread of formation times of
objects and on peculiar velocities of galaxy clusters.Comment: 11pp., 4 figures (available on request), LaTeX, BAP-04-1993-015-OA
The shape of high order correlation functions in CMB anisotropy maps
We present a phenomenological investigation of non-Gaussian effects that
could be seen on CMB temperature maps. Explicit expressions for the temperature
correlation functions are given for different types of primordial mode
couplings. We argue that a simplified description of the radial transfer
function for the temperature anisotropies allows to get insights into the
general properties of the bi and tri-spectra. The accuracy of these results is
explored together with the use of the small scale approximation to get explicit
expressions of high order spectra. The bi-spectrum is found to have alternate
signs for the successive acoustic peaks. Sign patterns for the trispectra are
more complicated and depend specifically on the type of metric couplings. Local
primordial couplings are found to give patterns that are different from those
expected from weak lensing effects.Comment: 31 pages, 17 figures, submitted to Phys. Rev.
Encircling the dark: constraining dark energy via cosmic density in spheres
The recently published analytic probability density function for the mildly
non-linear cosmic density field within spherical cells is used to build a
simple but accurate maximum likelihood estimate for the redshift evolution of
the variance of the density, which, as expected, is shown to have smaller
relative error than the sample variance. This estimator provides a competitive
probe for the equation of state of dark energy, reaching a few percent accuracy
on wp and wa for a Euclid-like survey. The corresponding likelihood function
can take into account the configuration of the cells via their relative
separations. A code to compute one-cell density probability density functions
for arbitrary initial power spectrum, top-hat smoothing and various spherical
collapse dynamics is made available online so as to provide straightforward
means of testing the effect of alternative dark energy models and initial
power-spectra on the low-redshift matter distribution.Comment: 7 pages, replaced to match the MNRAS accepted versio
Extended Perturbation Theory for the Local Density Distribution Function
Perturbation theory makes it possible to calculate the probability
distribution function (PDF) of the large scale density field in the small
variance limit. For top hat smoothing and scale-free Gaussian initial
fluctuations, the result depends only on the linear variance, sigma_linear, and
its logarithmic derivative with respect to the filtering scale
-(n_linear+3)=dlog sigma_linear^2/dlog L (Bernardeau 1994). In this paper, we
measure the PDF and its low-order moments in scale-free simulations evolved
well into the nonlinear regime and compare the results with the above
predictions, assuming that the spectral index and the variance are adjustable
parameters, n_eff and sigma_eff=sigma, where sigma is the true, nonlinear
variance. With these additional degrees of freedom, results from perturbation
theory provide a good fit of the PDFs, even in the highly nonlinear regime. The
value of n_eff is of course equal to n_linear when sigma << 1, and it decreases
with increasing sigma. A nearly flat plateau is reached when sigma >> 1. In
this regime, the difference between n_eff and n_linear increases when n_linear
decreases. For initial power-spectra with n_linear=-2,-1,0,+1, we find n_eff ~
-9,-3,-1,-0.5 when sigma^2 ~ 100.Comment: 13 pages, 6 figures, Latex (MN format), submitted to MNRA
Projection and Galaxy Clustering Fourier Spectra
Second order perturbation theory predicts a specific dependence of the
bispectrum, or three-point correlation function in the Fourier transform
domain, on the shape of the configuration of its three wave vector arguments,
which can be taken as a signature of structure formed by gravitational
instability. Comparing this known dependence on configuration shape with the
weak shape dependence of the galaxy bispectrum has been suggested as an
indication of bias in the galaxy distribution. However, to interpret results
obtained from projected catalogs, we must first understand the effects of
projection on this shape dependence. We present expressions for the projected
power spectrum and bispectrum in both Cartesian and spherical geometries, and
we examine the effects of projection on the predicted bispectrum with
particular attention to the dependence on configuration shape. Except for an
overall numerical factor, for Cartesian projection with characteristic depth
\Dstar there is little effect on the shape dependence of the bispectrum for
wavelengths small compared to \Dstar or projected wavenumbers q \Dstar
\gg 1 . For angular projection, a scaling law is found for spherical harmonic
index , but there is always a mixing of scales over the range of
the selection function. For large it is sufficient to examine a small
portion of the sky.Comment: aastex, 7 figure
High order correlation functions for self interacting scalar field in de Sitter space
We present the expressions of the three- and four-point correlation functions
of a self interacting light scalar field in a de Sitter spacetime at tree order
respectively for a cubic and a quartic potential. Exact expressions are derived
and their limiting behaviour on super-horizon scales are presented. Their
essential features are shown to be similar to those obtained in a classical
approach.Comment: 8 pages, 4 figure
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
Observational Constraints on Higher Order Clustering up to $z\simeq 1
Constraints on the validity of the hierarchical gravitational instability
theory and the evolution of biasing are presented based upon measurements of
higher order clustering statistics in the Deeprange Survey, a catalog of
galaxies with derived from a KPNO 4m CCD imaging
survey of a contiguous region. We compute the
3-point and 4-point angular correlation functions using a direct estimation for
the former and the counts-in-cells technique for both. The skewness
decreases by a factor of as galaxy magnitude increases over the
range (). This decrease is
consistent with a small {\it increase} of the bias with increasing redshift,
but not by more than a factor of 2 for the highest redshifts probed. Our
results are strongly inconsistent, at about the level, with
typical cosmic string models in which the initial perturbations follow a
non-Gaussian distribution - such models generally predict an opposite trend in
the degree of bias as a function of redshift. We also find that the scaling
relation between the 3-point and 4-point correlation functions remains
approximately invariant over the above magnitude range. The simplest model that
is consistent with these constraints is a universe in which an initially
Gaussian perturbation spectrum evolves under the influence of gravity combined
with a low level of bias between the matter and the galaxies that decreases
slightly from to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change
Structure formation from non-Gaussian initial conditions: multivariate biasing, statistics, and comparison with N-body simulations
We study structure formation in the presence of primordial non-Gaussianity of
the local type with parameters f_NL and g_NL. We show that the distribution of
dark-matter halos is naturally described by a multivariate bias scheme where
the halo overdensity depends not only on the underlying matter density
fluctuation delta, but also on the Gaussian part of the primordial
gravitational potential phi. This corresponds to a non-local bias scheme in
terms of delta only. We derive the coefficients of the bias expansion as a
function of the halo mass by applying the peak-background split to common
parametrizations for the halo mass function in the non-Gaussian scenario. We
then compute the halo power spectrum and halo-matter cross spectrum in the
framework of Eulerian perturbation theory up to third order. Comparing our
results against N-body simulations, we find that our model accurately describes
the numerical data for wavenumbers k < 0.1-0.3 h/Mpc depending on redshift and
halo mass. In our multivariate approach, perturbations in the halo counts trace
phi on large scales and this explains why the halo and matter power spectra
show different asymptotic trends for k -> 0. This strongly scale-dependent bias
originates from terms at leading order in our expansion. This is different from
what happens using the standard univariate local bias where the scale-dependent
terms come from badly behaved higher-order corrections. On the other hand, our
biasing scheme reduces to the usual local bias on smaller scales where |phi| is
typically much smaller than the density perturbations. We finally discuss the
halo bispectrum in the context of multivariate biasing and show that, due to
its strong scale and shape dependence, it is a powerful tool for the detection
of primordial non-Gaussianity from future galaxy surveys.Comment: 26 pages, 16 figures. Minor modifications, version accepted by Phys.
Rev.
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