Related papers: xPand: An algorithm for perturbing homogeneous cos…
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any…
We show that in four or more spacetime dimensions, the Einstein equations for gravitational perturbations of maximally symmetric vacuum black holes can be reduced to a single 2nd-order wave equation in a two-dimensional static spacetime for…
In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides…
We discuss a gauge invariant approach to the theory of cosmological perturbations in a higher-dimensonal background. We find the normal modes which diagonalize the perturbed action, for a scalar field minimally coupled to gravity, in a…
The paper presents results for deriving closed-form analytic solutions of the non-relativistic linear perturbation equations, which govern the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model.…
We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the…
Using the gradient expansion approach, we formulate a nonlinear cosmological perturbation theory on super-horizon scales valid to $O(\epsilon^2)$, where $\epsilon$ is the expansion parameter associated with a spatial derivative. For…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
In this paper the scalar-tensor theory is applied to the study of perturbations in a multi-fluid universe, using the 1+3 covariant approach. Both scalar and harmonic decompositions are instituted on the perturbation equations. In…
We develop a spectral method for the spatially homogeneous Boltzmann equation using Burnett polynomials in the basis functions. Using the sparsity of the coefficients in the expansion of the collision term, the computational cost is reduced…
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity…
We develop a systematic classical framework to accommodate canonical quantization of geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existing approach of standard cosmological perturbations is…
We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…
In this work, our aim is to obtain a Hamiltonian formulation suitable for canonical quantization. Moreover, we assume that the early Universe can be described with fewer initial symmetries, thus we abandon the isotropy assumption and…