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The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation…
In this paper, we describe the first steps towards fully non-perturbative cosmology. We explain why the conventional methods used by cosmologists based on the ADM formulation are generally inadequate for this purpose and why it is…
The evolution of baryon density perturbations on very small scales is investigated. In particular, the nonlinear growth induced by the radiation drag force from the shear velocity field on larger scales during the recombination epoch, which…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our…
In this thesis we present research into linear perturbations in Lemaitre-Tolman-Bondi (LTB) and Assisted Coupled Quintessence (ACQ) Cosmologies. First we give a brief overview of the standard model of cosmology. We then introduce…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
Using a gauge-invariant formalism we derive and solve the perturbed cosmological equations for the BSBM theory of varying fine structure 'constant'. We calculate the time evolution of inhomogeneous perturbations of the fine structure…
In the Gaia era, understanding the effects of the perturbations of the Galactic disc is of major importance in the context of dynamical modelling. In this theoretical paper we extend previous work in which, making use of the epicyclic…
Cosmography has been extensively utilized to constrain the kinematic state of the Universe using measured distances. In this work, we propose a new method to reconstruct coupling theories using the first kind of Chebyshev polynomial for two…
Spectroscopy infers the internal structure of physical systems by measuring their response to perturbations. We apply this principle to neural networks: perturbing the data distribution by upweighting a token $y$ in context $x$, we measure…
The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In…
The dark energy plus cold dark matter ($\Lambda$CDM) cosmological model has been a demonstrably successful framework for predicting and explaining the large-scale structure of Universe and its evolution with time. Yet on length scales…
There has been some recent activity in trying to understand the dark matter clustering properties in the quasilinear regime, through resummation of perturbative terms, otherwise known as the renormalized perturbation theory…
Cosmic voids in the large-scale structure of the Universe affect the peculiar motions of objects in their vicinity. Although these motions are difficult to observe directly, the clustering pattern of their surrounding tracers in redshift…
We develop a dark-sector selective trace-coupled extension of gravity in which the matter--curvature coupling depends exclusively on the trace of the dark-matter energy--momentum tensor, $T_{\chi}$, defined from a canonical dark-matter…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
The $\Lambda$CDM model has long served as the cornerstone of modern cosmology, offering an elegant and successful framework for interpreting a wide range of cosmological observations. However, the rise of high-precision datasets has…
We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate…
In a perturbed Universe, comoving tracers on a two-dimensional surface of constant observed redshift are at different proper time since the Big Bang. For tracers whose age is known independently, one can measure these perturbations of the…