Related papers: Numerical Relativity as a New Tool for Fundamental…
Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating \emph{a priori} any particular cosmological model. All quantities of interest are expanded as a Taylor series around…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this…
From the standpoint of theoretical physics we can treat Newtonian cosmology as a problem in nonlinear dynamics. The attempt to average the density, in search of a method of making contact between theory and observation, is replaced by the…
Numerical simulations are a versatile tool providing insight into the complicated process of structure formation in cosmology. This process is mainly governed by gravity, which is the dominant force on large scales. To date, a century after…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an…
The theory of cosmological perturbations has become a cornerstone of modern quantitative cosmology since it is the framework which provides the link between the models of the very early Universe such as the inflationary Universe scenario…
We explore a cosmological model in which dark matter is non-minimally coupled to gravity at the fluid level. While typically subdominant compared to Standard Model forces, such couplings may dominate dark matter dynamics. We show that this…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
Models of inflationary cosmology admit a choice of the metric for which the geometry of homogeneous isotropic solutions becomes flat Minkowski space in the infinite past. In this primordial flat frame all mass scales vanish in the infinite…
Dark energy is one of the deepest puzzles in modern cosmology, and mounting evidence suggests that it is not just a cosmological constant but a genuinely dynamical component. Although cosmology and dynamical systems theory emerged from…
Observational Cosmology has indeed made very rapid progress in the past decade. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and,…
We explore nonlocally modified models of gravity, inspired by quantum loop corrections, as a mechanism for explaining current cosmic acceleration. These theories enjoy two major advantages: they allow a delayed response to cosmic events,…
We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…
Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of…