19 research outputs found
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
General CMB bispectrum analysis using wavelets and separable modes
In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. This will be particularly important for upcoming surveys such as \emph{Planck}. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding \fnllocal=38.4 \pm 23.6 and \fnlequil=-119.2 \pm 123.6
Towards optimal cosmological parameter recovery from compressed bispectrum statistics
Over the next decade, improvements in cosmological parameter constraints will be driven by surveys of large-scale structure in the Universe. The information they contain can be measured by suitably-chosen correlation functions, and the non-linearity of structure formation implies that significant information will be carried by the three-point function or higher correlators. Extracting this information is extremely challenging, requiring accurate modelling and significant computational resources to estimate the covariance matrix describing correlation between different Fourier configurations. We investigate whether it is possible to reduce this matrix without significant loss of information by using a proxy that aggregates the bispectrum over a subset of configurations. Specifically, we study constraints on ΞCDM parameters from a future galaxy survey combining the power spectrum with (a) the integrated bispectrum, (b) the line correlation function and (c) the modal decomposition of the bispectrum. We include a simple estimate for the degradation of the bispectrum with shot noise. Our results demonstrate that the modal bispectrum has comparable performance to the Fourier bispectrum, even using considerably fewer modes than Fourier configurations. The line correlation function has good performance, but is less effective. The integrated bispectrum is comparatively insensitive to the background cosmology. Addition of bispectrum data can improve constraints on bias parameters and Ο8 by a factor between 3 and 5 compared to power spectrum measurements alone. For other parameters, improvements of up to βΌ 20% are possible. Finally, we use a range of theoretical models to explore the sophistication required to produce realistic predictions for each proxy
Implications of the cosmic microwave background power asymmetry for the early universe
Observations of the microwave background fluctuations suggest a
scale-dependent amplitude asymmetry of roughly 2.5 sigma significance.
Inflationary explanations for this 'anomaly' require non-Gaussian fluctuations
which couple observable modes to those on much larger scales. In this Letter we
describe an analysis of such scenarios which significantly extends previous
treatments. We identify the non-Gaussian 'response function' which
characterizes the asymmetry, and show that it is non-trivial to construct a
model which yields a sufficient amplitude: many independent fine tunings are
required, often making such models appear less likely than the anomaly they
seek to explain. We present an explicit model satisfying observational
constraints and determine for the first time how large its bispectrum would
appear to a Planck-like experiment. Although this model is merely illustrative,
we expect it is a good proxy for the bispectrum in a sizeable class of models
which generate a scale-dependent response using a large eta parameter.Comment: 5 pages. v2: Minor changes to match version published in Phys. Rev.
The bispectrum of matter perturbations from cosmic strings
We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings
CMB lensing and primordial squeezed non-Gaussianity
Squeezed primordial non-Gaussianity can strongly constrain early-universe
physics, but it can only be observed on the CMB after it has been
gravitationally lensed. We give a new simple non-perturbative prescription for
accurately calculating the effect of lensing on any squeezed primordial
bispectrum shape, and test it with simulations. We give the generalization to
polarization bispectra, and discuss the effect of lensing on the trispectrum.
We explain why neglecting the lensing smoothing effect does not significantly
bias estimators of local primordial non-Gaussianity, even though the change in
shape can be >~10%. We also show how tau_NL trispectrum estimators can be well
approximated by much simpler CMB temperature modulation estimators, and hence
that there is potentially a ~10-30% bias due to very large-scale lensing modes,
depending on the range of modulation scales included. Including dipole sky
modulations can halve the tau_NL error bar if kinematic effects can be
subtracted using known properties of the CMB temperature dipole. Lensing
effects on the g_NL trispectrum are small compared to the error bar. In
appendices we give the general result for lensing of any primordial bispectrum,
and show how any full-sky squeezed bispectrum can be decomposed into orthogonal
modes of distinct angular dependence.Comment: 22 pages, 6 figures; minor edits to match published versio
Impact of bias and redshift-space modelling for the halo power spectrum: testing the effective field theory of large-scale structure
We study the impact of different bias and redshift-space models on the halo power spectrum, quantifying their effect by comparing the fit to a subset of realizations taken from the WizCOLA suite. These provide simulated power spectrum measurements between kmin = 0.03 h/Mpc and kmax = 0.29 h/Mpc, constructed using the comoving Lagrangian acceleration method. For the bias prescription we include (i) simple linear bias; (ii) the McDonald & Roy model and (iii) its coevolution variant introduced by Saito et al.; and (iv) a very general model including all terms up to one-loop and corrections from advection. For the redshift-space modelling we include the Kaiser formula with exponential damping and the power spectrum provided by (i) tree-level perturbation theory and (ii) the Halofit prescription; (iii) one-loop perturbation theory, also with exponential damping; and (iv) an effective field theory description, also at one-loop, with damping represented by the EFT subtractions. We quantify the improvement from each layer of modelling by measuring the typical improvement in Ο2 when fitting to a member of the simulation suite. We attempt to detect overfitting by testing for compatibility between the best-fit power spectrum per realization and the best-fit over the entire WizCOLA suite. For both bias and the redshift-space map we find that increasingly permissive models yield improvements in Ο2 but with diminishing returns. The most permissive models show modest evidence for overfitting. Accounting for model complexity using the Bayesian Information Criterion, we argue that standard perturbation theory up to one-loop, or a related model such as that of Taruya, Nishimichi & Saito, coupled to the Saito et al. coevolution bias model, is likely to provide a good compromise for near-future galaxy surveys operating with comparable kmax
Constraining Galileon inflation
In this short paper, we present constraints on the Galileon inflationary model from the CMB bispectrum. We employ a principal-component analysis of the independent degrees of freedom constrained by data and apply this to the WMAP 9-year data to constrain the free parameters of the model. A simple Bayesian comparison establishes that support for the Galileon model from bispectrum data is at best weak