Carlos Garcia-Garcia

Abstract:

Cosmic shear is one of the most powerful probes of Dark Energy, targeted by several current and future galaxy surveys. Lensing shear, however, is only sampled at the positions of galaxies with measured shapes in the catalog, making its associated sky window function one of the most complicated amongst all projected cosmological probes of inhomogeneities, as well as giving rise to inhomogeneous noise. Partly for this reason, cosmic shear analyses have been mostly carried out in real-space, making use of correlation functions, as opposed to Fourier-space power spectra. Since the use of power spectra can yield complementary information and has numerical advantages over real-space pipelines, it is important to develop a complete formalism describing the standard unbiased power spectrum estimators as well as their associated uncertainties. Building on previous work, this paper contains a study of the main complications associated with estimating and interpreting shear power spectra, and presents fast and accurate methods to estimate two key quantities needed for their practical usage: the noise bias and the Gaussian covariance matrix, fully accounting for survey geometry, with some of these results also applicable to other cosmological probes. We demonstrate the performance of these methods by applying them to the latest public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting power spectra, covariance matrices, null tests and all associated data necessary for a full cosmological analysis publicly available.

Abstract:

The late time acceleration of the Universe can be characterized in terms of an extra, time-dependent, component of the Universe—dark energy. The simplest proposal for dark energy is a scalar-tensor theory—quintessence—which consists of a scalar field, ϕ, whose dynamics is solely dictated by its potential, V(ϕ). Such a theory can be uniquely characterized by the equation of state of the scalar field energy momentum-tensor. We find the time dependence of the equation of state for a broad family of potentials and, using this information, we propose an analytic prior distribution for the most commonly used parametrization. We show that this analytic prior can be used to accurately predict the distribution of observables for the next generation of cosmological surveys. Including the theoretical priors in the comparison with observations considerably improves the constraints on the equation of state.

Abstract:

The disconnected part of the power spectrum covariance matrix (also known as the "Gaussian" covariance) is the dominant contribution on large scales for galaxy clustering and weak lensing datasets. The presence of a complicated sky mask causes non-trivial correlations between different Fourier/harmonic modes, which must be accurately characterized in order to obtain reliable cosmological constraints. This is particularly relevant for galaxy survey data. Unfortunately, an exact calculation of these correlations involves O(ℓmax6) operations that become computationally impractical very quickly. We present an implementation of approximate methods to estimate the Gaussian covariance matrix of power spectra involving spin-0 and spin-2 flat- and curved-sky fields, expanding on existing algorithms {developed in the context of CMB analyses}. These methods achieve an O(ℓmax3) scaling, which makes the computation of the covariance matrix as fast as the computation of the power spectrum itself. We quantify the accuracy of these methods on large-scale structure and weak lensing data, making use of a large number of Gaussian but otherwise realistic simulations. We show that, using the approximate covariance matrix, we are able to recover the true posterior distribution of cosmological parameters to high accuracy. We also quantify the shortcomings of these methods, which become unreliable on the very largest scales, as well as for covariance matrix elements involving cosmic shear B modes. The algorithms presented here are implemented in the public code NaMaster https://github.com/LSSTDESC/NaMaster.