89 research outputs found
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
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
Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D
The thermal Sunyaev-Zel'dovich (tSZ) effect measures the line-of-sight
projection of the thermal pressure of free electrons and lacks any redshift
information. By cross correlating the tSZ effect with an external cosmological
tracer we can recover a good fraction of this lost information. Weak lensing
(WL) is thought to provide an unbiased probe of the dark Universe, with many WL
surveys having sky coverage that overlaps with tSZ surveys. Generalising the
tomographic approach, we advocate the use of the spherical Fourier-Bessel (sFB)
expansion to perform an analysis of the cross-correlation between the projected
(2D) tSZ Compton -parameter maps and 3D weak lensing convergence maps. We
use redshift dependent linear biasing and the halo model as a tool to
investigate the tSZ-WL cross-correlations in 3D. We use the Press-Schechter
(PS) and the Sheth-Tormen (ST) mass-functions in our calculations, finding that
the results are quite sensitive to detailed modelling. We provide detailed
analysis of surveys with photometric and spectroscopic redshifts. The
signal-to-noise (S/N) of the cross-spectra for
individual 3D modes, defined by the radial and tangential wave numbers
, remains comparable to, but below, unity though optimal binning is
expected to improve this. The results presented can be generalised to analyse
other CMB secondaries, such as the kinetic Sunyaev-Zel'dovich (kSZ) effect.Comment: 27 pages, 12 Figures. Published in MNRA
Principal Components of CMB non-Gaussianity
The skew-spectrum statistic introduced by Munshi & Heavens (2010) has
recently been used in studies of non-Gaussianity from diverse cosmological data
sets including the detection of primary and secondary non-Gaussianity of Cosmic
Microwave Background (CMB) radiation. Extending previous work, focussed on
independent estimation, here we deal with the question of joint estimation of
multiple skew-spectra from the same or correlated data sets. We consider the
optimum skew-spectra for various models of primordial non-Gaussianity as well
as secondary bispectra that originate from the cross-correlation of secondaries
and lensing of CMB: coupling of lensing with the Integrated Sachs-Wolfe (ISW)
effect, coupling of lensing with thermal Sunyaev-Zeldovich (tSZ), as well as
from unresolved point-sources (PS). For joint estimation of various types of
non-Gaussianity, we use the PCA to construct the linear combinations of
amplitudes of various models of non-Gaussianity, e.g. that can be estimated from CMB
maps. Bias induced in the estimation of primordial non-Gaussianity due to
secondary non-Gaussianity is evaluated. The PCA approach allows one to infer
approximate (but generally accurate) constraints using CMB data sets on any
reasonably smooth model by use of a lookup table and performing a simple
computation. This principle is validated by computing constraints on the DBI
bispectrum using a PCA analysis of the standard templates.Comment: 17 pages, 5 figures, 4 tables. Matches published versio
Consistency Relations in Effective Field Theory
The consistency relations in large scale structure relate the lower-order
correlation functions with their higher-order counterparts. They are direct
outcome of the underlying symmetries of a dynamical system and can be tested
using data from future surveys such as Euclid. Using techniques from standard
perturbation theory (SPT), previous studies of consistency relation have
concentrated on continuity-momentum (Euler)-Poisson system of an ideal fluid.
We investigate the consistency relations in effective field theory (EFT) which
adjusts the SPT predictions to account for the departure from the ideal fluid
description on small scales. We provide detailed results for the 3D density
contrast as well as the {\em scaled} divergence of velocity
. Assuming a CDM background cosmology, we find the
correction to SPT results becomes important at and
that the suppression from EFT to SPT results that scales as square of the wave
number , can reach of the total at at
. We have also investigated whether effective field theory corrections to
models of primordial non-Gaussianity can alter the squeezed limit behaviour,
finding the results to be rather insensitive to these counterterms. In
addition, we present the EFT corrections to the squeezed limit of the
bispectrum in redshift space which may be of interest for tests of theories of
modified gravity.Comment: 23 pages + bibliography, 6 figures. Minor changes to match version
accepted for publication by JCA
The Statistics of Cosmological Lyman-alpha Absorption
We study the effect of the non-Gaussianity induced by gravitational evolution
upon the statistical properties of absorption in quasar (QSO) spectra. Using
the generic hierarchical ansatz and the lognormal approximation we derive the
analytical expressions for the one-point PDF as well as for the joint two-point
probability distribution (2PDF) of transmitted fluxes in two neighbouring QSOs.
These flux PDFs are constructed in 3D as well as in projection (i.e. in 2D).
The PDFs are constructed by relating the lower-order moments, i.e. cumulants
and cumulant correlators, of the fluxes to the 3D neutral hydrogen distribution
which is, in turn, expressed as a function of the underlying dark matter
distribution. The lower-order moments are next modelled using a generating
function formalism in the context of a {\em minimal tree-model} for the
higher-order correlation hierarchy. These different approximations give nearly
identical results for the range of redshifts probed, and we also find a very
good agreement between our predictions and outputs of hydrodynamical
simulations. The formalism developed here for the joint statistics of
flux-decrements concerning two lines of sight can be extended to multiple lines
of sight, which could be particularly important for the 3D reconstruction of
the cosmic web from QSO spectra (e.g. in the BOSS survey). These statistics
probe the underlying projected neutral hydrogen field and are thus linked to
"hot-spots" of absorption. The results for the PDF and the bias presented here
use the same functional forms of scaling functions that have previously been
employed for the modelling of other cosmological observation such as the
Sunyaev-Zel'dovich effect.Comment: 17 pages, 8 figure
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