Dynamical dark energy models

Abstract

Ever since it was discovered that the Universe is expanding at an accelerated rate, cosmologists have been searching for an explanation in the form of dark energy: a mechanism or physical component capable of producing this effect. The study presented here focuses on dynamical dark energy models, in which the observed acceleration arises as a result of either a cosmic component whose pressure is negative, or as a modification to the General Relativistic description of the geometry of the space-time manifold. The word ‘dynamical’ sets these models apart from the ΛCDM cosmology, in which the density of dark energy remains constant as the Universe expands. Many works in the literature are based on the premise of a spatially flat Universe, and indeed this is what observational data appears to point to in a ΛCDM framework. The question naturally arises, however, whether the assumption of flatness continues to hold in the case of dynamical dark energy models, especially since spatial curvature is often correlated with dark energy parameters, and so any wrong assumptions about it could greatly distort our understanding of dark energy. The aim of this thesis is precisely to look for an answer to that question. For the first part of the study, dark energy is modelled as a scalar field that can either be minimally or non-minimally coupled to the Ricci scalar, and a number of exact solutions to the cosmological field equations are presented. Each corresponds to a particular geometry – flat, open or closed. In the next part, analytical methods are combined with numerical techniques to analyse several models from the literature, chosen for their ability to represent the complete cosmic history. The aim is to investigate how spatial curvature influences the main features of the evolution. Initially, the Universe is assumed to consist of a Vander Waalsfluid, but this alone cannot provide an explanation for the acceleration at late times, despite the fact that it accounts for the inflationary and matter-dominated epochs. Hence, dark energy is introduced as Quintessence, a Chaplygin gas or dynamical vacuum energy. It turns out that the transition from the inflationary epoch to the matter-dominated one would occur first for the open universe, and last for the closed one. The onset of late-time acceleration would also take place in this order. Furthermore, positive curvature is found to enhance inflationary acceleration and the deceleration that follows. Among the fluid characteristics considered are the customary proportionality between energy density and pressure, and bulk viscosity. The effects of spatial curvature on cosmic evolution are then investigated in the context of the generalised running vacuum model (GRVM) and its sub-cases. In the GRVM, the cosmological constant is replaced by a function of the Hubble parameter and its time derivative: Λ(H) = A + BH2 + C ˙ H (A, B and C being constants). Two parameter models are obtained by setting B or C equal to zero. The main goal is to find out if the models best describe observations when one assumes spatial flatness, or if the presence of curvature improves the fit. This is accomplished via a Markov Chain Monte Carlo (MCMC) analysis. The data set used comprises measurements of observables related to Type-Ia supernovae, cosmic clocks, baryon acoustic oscillations, the cosmic microwave background and redshift-space distortions (RSDs). Since it is well known that the data itself (rather than just the particular model) plays an important part in determining whether curvature is ruled out, the chapter draws comparisonsbetweentheconstraintsobtainedinvariousscenarios,suchaswhenRSD measurements are excluded (in contrast to when the full data set is employed). The lack of consensus within the scientific community about the value of the Hubble constant(H0) is also taken into account. Two different values of H0 from the literature are introduced and their effects on the results are investigated. In the last part, the focus is shifted to an alternative theory of gravity – namely, f(R) gravity, constructed by generalising the Ricci scalar in the Einstein-Hilbert action to a function thereof. Four f(R) models are considered, all of which appear to be compatible with Solar-System and cosmological constraints: the Hu-Sawicki, Starobinsky, Exponential and Tsujikawa models. The idea is to see whether these models are able to accommodate non-zero spatial curvature (while still being consistent with cosmological observations). Since they all reduce to ΛCD Mathigh redshifts, any differences from ΛCDM are most likely to emerge at the level of perturbations. Therefore, the perturbation equations (in the sub-Hubble, quasi-static regime) are derived and incorporated into the analysis, which is again carried out using MCMC sampling techniques. Given that matter density perturbations are scale-dependent in f(R) gravity, the results obtained for different values of k† (the comoving wave number) are compared.