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The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate, and geometry of the Universe, and hence can be used to measure key cosmological parameters. In a homogeneous Universe the…
Upcoming surveys of cosmic structures will probe scales close to the cosmological horizon, which opens up new opportunities for testing the cosmological concordance model to high accuracy. In particular, constraints on the squeezed…
A large fraction of the information collected by cosmological surveys is simply discarded to avoid lengthscales which are difficult to model theoretically. We introduce a new technique which enables the extraction of useful information from…
Modelling of the weak lensing of the CMB will be crucial to obtain correct cosmological parameter constraints from forthcoming precision CMB anisotropy observations. The lensing affects the power spectrum as well as inducing…
Over the next decade, improvements in cosmological parameter constraints will be driven by surveys of large-scale structure. Its inherent non-linearity suggests that significant information will be embedded in higher correlations beyond the…
We present a novel method to compress galaxy clustering three-point statistics and apply it to redshift space galaxy bispectrum monopole measurements from BOSS DR12 CMASS data considering a $k$-space range of $0.03-0.12\,h/\mathrm{Mpc}$.…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
Over the last decade, measurements of the CMB anisotropy has spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic effects in the increasingly sensitive, high resolution, `full' sky…
We describe the details of the binned bispectrum estimator as used for the official 2013 and 2015 analyses of the temperature and polarization CMB maps from the ESA Planck satellite. The defining aspect of this estimator is the…
In this paper we establish the accuracy and robustness of a fast estimator for the bispectrum - the "FFT bispectrum estimator". The implementation of the estimator presented here offers speed and simplicity benefits over a direct sampling…
Higher-order correlation functions of the large-scale galaxy distribution offer access to information beyond that contained in standard 2-point statistics such as the power spectrum. In this work we assess this potential for the…
The primary results of most observations of cosmic microwave background (CMB) anisotropy are estimates of the angular power spectrum averaged through some broad band, called band-powers. These estimates are in turn what are used to produce…
To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to…
The two-point summary statistics is one of the most commonly used tools in the study of cosmological structure. Starting from the theoretical power spectrum defined in the 3D volume and obtained via the process of ensemble averaging, we…
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the…
The bispectrum of the microwave background sky is a possible discriminator between inflationary and defect models of structure formation in the Universe. The bispectrum, which is the analogue of the temperature 3-point correlation function…
We develop a new method for deconvolving the smearing effect of the survey window in the analysis of the galaxy multipole power spectra from a redshift survey. This method is based on the deconvolution theorem, and is compatible with the…
We investigate the effect of the window function on the multipole power spectrum in two different ways. First, we consider the convolved power spectrum including the window effect, which is obtained by following the familiar (FKP) method…
We measure the power spectrum of the galaxy distribution in the ESO Slice Project (ESP) galaxy redshift survey. We develope a technique to describe the survey window function analytically, and then deconvolve it from the measured power…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…