8,835 research outputs found
Covariance of Weak Lensing Observables
Analytical expressions for covariances of weak lensing statistics related to
the aperture mass \Map are derived for realistic survey geometries such as
SNAP for a range of smoothing angles and redshift bins. We incorporate the
contributions to the noise due to the intrinsic ellipticity distribution and
the effects of finite size of the catalogue. Extending previous results to the
most general case where the overlap of source populations is included in a
complete analysis of error estimates, we study how various angular scales in
various redshifts are correlated and how the estimation scatter changes with
survey parameters. Dependence on cosmological parameters and source redshift
distributions are studied in detail. Numerical simulations are used to test the
validity of various ingredients to our calculations. Correlation coefficients
are defined in a way that makes them practically independent of cosmology. They
can provide important tools to cross-correlate one or more different surveys,
as well as various redshift bins within the same survey or various angular
scales from same or different surveys. Dependence of these coefficients on
various models of underlying mass correlation hierarchy is also studied.
Generalisations of these coefficients at the level of three-point statistics
have the potential to probe the complete shape dependence of the underlying
bi-spectrum of the matter distribution. A complete error analysis incorporating
all sources of errors suggest encouraging results for studies using future
space based weak lensing surveys such as SNAP.Comment: 14 pages, 10 Figures, Submitted to MNRA
Higher-order Statistics of Weak Lensing Shear and Flexion
Owing to their more extensive sky coverage and tighter control on systematic
errors, future deep weak lensing surveys should provide a better statistical
picture of the dark matter clustering beyond the level of the power spectrum.
In this context, the study of non-Gaussianity induced by gravity can help
tighten constraints on the background cosmology by breaking parameter
degeneracies, as well as throwing light on the nature of dark matter, dark
energy or alternative gravity theories. Analysis of the shear or flexion
properties of such maps is more complicated than the simpler case of the
convergence due to the spinorial nature of the fields involved. Here we develop
analytical tools for the study of higher-order statistics such as the
bispectrum (or trispectrum) directly using such maps at different source
redshift. The statistics we introduce can be constructed from cumulants of the
shear or flexions, involving the cross-correlation of squared and cubic maps at
different redshifts. Typically, the low signal-to-noise ratio prevents recovery
of the bispectrum or trispectrum mode by mode. We define power spectra
associated with each multi- spectra which compresses some of the available
information of higher order multispectra. We show how these can be recovered
from a noisy observational data even in the presence of arbitrary mask, which
introduces mixing between Electric (E-type) and Magnetic (B-type) polarization,
in an unbiased way. We also introduce higher order cross-correlators which can
cross-correlate lensing shear with different tracers of large scale structures.Comment: 16 pages, 2 figure
Higher-order Convergence Statistics for Three-dimensional Weak Gravitational Lensing
Weak gravitational lensing on a cosmological scales can provide strong
constraints both on the nature of dark matter and the dark energy equation of
state. Most current weak lensing studies are restricted to (two-dimensional)
projections, but tomographic studies with photometric redshifts have started,
and future surveys offer the possibility of probing the evolution of structure
with redshift. In future we will be able to probe the growth of structure in 3D
and put tighter constraints on cosmological models than can be achieved by the
use of galaxy redshift surveys alone. Earlier studies in this direction focused
mainly on evolution of the 3D power spectrum, but extension to higher-order
statistics can lift degeneracies as well as providing information on primordial
non-gaussianity. We present analytical results for specific higher-order
descriptors, the bispectrum and trispectrum, as well as collapsed multi-point
statistics derived from them, i.e. cumulant correlators. We also compute
quantities we call the power spectra associated with the bispectrum and
trispectrum, the Fourier transforms of the well-known cumulant correlators. We
compute the redshift dependence of these objects and study their performance in
the presence of realistic noise and photometric redshift errors.Comment: 21 page
Shifted convolution sums for
For the shifted convolution sum where
are the Fourier coefficients of a Maass form
, and are those of a Maass or
holomorphic form , and , we establish
the bound
The bound is uniform with respect to the shift
Symmetries, Invariants and Generating Functions: Higher-order Statistics of Biased Tracers
Gravitationally collapsed objects are known to be biased tracers of an
underlying density contrast. Using symmetry arguments, generalised biasing
schemes have recently been developed to relate the halo density contrast
with the underlying density contrast , divergence of
velocity and their higher-order derivatives. This is done by
constructing invariants such as . We show how the generating
function formalism in Eulerian standard perturbation theory (SPT) can be used
to show that many of the additional terms based on extended Galilean and
Lifshitz symmetry actually do not make any contribution to the higher-order
statistics of biased tracers. Other terms can also be drastically simplified
allowing us to write the vertices associated with in terms of the
vertices of and , the higher-order derivatives and the bias
coefficients. We also compute the cumulant correlators (CCs) for two different
tracer populations. These perturbative results are valid for tree-level
contributions but at an arbitrary order. We also take into account the
stochastic nature bias in our analysis. Extending previous results of a local
polynomial model of bias, we express the one-point cumulants and
their two-point counterparts, the CCs i.e. , of biased tracers
in terms of that of their underlying density contrast counterparts. As a
by-product of our calculation we also discuss the results using approximations
based on Lagrangian perturbation theory (LPT).Comment: 15 page
From Weak Lensing to non-Gaussianity via Minkowski Functionals
We present a new harmonic-domain approach for extracting morphological
information, in the form of Minkowski Functionals (MFs), from weak lensing (WL)
convergence maps. Using a perturbative expansion of the MFs, which is expected
to be valid for the range of angular scales probed by most current weak-lensing
surveys, we show that the study of three generalized skewness parameters is
equivalent to the study of the three MFs defined in two dimensions. We then
extend these skewness parameters to three associated skew-spectra which carry
more information about the convergence bispectrum than their one-point
counterparts. We discuss various issues such as noise and incomplete sky
coverage in the context of estimation of these skew-spectra from realistic
data. Our technique provides an alternative to the pixel-space approaches
typically used in the estimation of MFs, and it can be particularly useful in
the presence of masks with non-trivial topology. Analytical modeling of weak
lensing statistics relies on an accurate modeling of the statistics of
underlying density distribution. We apply three different formalisms to model
the underlying dark-matter bispectrum: the hierarchical ansatz, halo model and
a fitting function based on numerical simulations; MFs resulting from each of
these formalisms are computed and compared. We investigate the extent to witch
late-time gravity-induced non-Gaussianity (to which weak lensing is primarily
sensitive) can be separated from primordial non-Gaussianity and how this
separation depends on source redshift and angular scale.Comment: 22 Pages, 12 Figures. Submitting To MNRA
Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
Gravitational clustering in the nonlinear regime remains poorly understood.
Gravity dual of gravitational clustering has recently been proposed as a means
to study the nonlinear regime. The stable clustering ansatz remains a key
ingredient to our understanding of gravitational clustering in the highly
nonlinear regime. We study certain aspects of violation of the stable
clustering ansatz in the gravity dual of Large Scale Structure (LSS). We extend
the recent studies of gravitational clustering using AdS gravity dual to take
into account possible departure from the stable clustering ansatz and to
arbitrary dimensions. Next, we extend the recently introduced consistency
relations to arbitrary dimensions. We use the consistency relations to test the
commonly used models of gravitational clustering including the halo models and
hierarchical ans\"atze. In particular we establish a tower of consistency
relations for the hierarchical amplitudes: etc. as a
functions of the scaled peculiar velocity . We also study the variants of
popular halo models in this context. In contrast to recent claims, none of
these models, in their simplest incarnation, seem to satisfy the consistency
relations in the soft limit.Comment: 21 pages, 4 figure
The circle method and bounds for -functions - I
Let be a Hecke-Maass or holomorphic primitive cusp form of arbitrary
level and nebentypus, and let be a primitive character of conductor .
For the twisted -function we establish the hybrid
subconvex bound for . The implied constant depends only on the form and
.Comment: 8 page
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