NUMERICAL STUDY OF A PERTURBED EINSTEIN-DESITTER COSMOLOGICAL MODEL

Given the ever-increasing scale of structures discovered in the universe, we solve Einstein's equations numerically, under simplifying assumptions, to examine how this lack of uniformity affects the metric of Einstein-de Sitter cosmology. The results confirm the qualitative conclusion of Barrow, that a large density contrast is compatible with much smaller metric perturbations. The contribution of this peculiar gravity to the redshift might complicate studies of peculiar motions of galaxies, although it appears that the distortion is small for nearby clusters.

General properties of cosmological models with an isotropic singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a gamma-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.

An analysis of helium primordial nucleosynthesis with a variable cosmological coupling

The synthesis of helium in the early Universe depends on many input parameters, including the value of the gravitational coupling during the period when the nucleosynthesis takes place. We compute the primordial abundance of helium as function of the gravitational coupling, using a semi-analytical method, in order to track the influence of G in the primordial nucleosynthesis. To be specific, we construct a cosmological model with varying G, using the Brans-Dicke theory. The greater the value of G at nucleosynthesis period, the greater the predicted abundance of helium. Using the observational data for the abundance of primordial helium, constraints for the time variation of G are established.

Stochastic semiclassical cosmological models

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless nonconformal matter fields in the early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so-called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological model introduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.

Particle creation due to cosmological contraction of extra dimensions

Particle production in a cosmological spacetime with extra dimensions is discussed. A five-dimensional cosmological model with a three-dimensional space expanding isotropically like in a radiative Friedmann-Robertson-Walker model and an internal space contracting to a constant small size is considered. The parameters of the model are adjusted so that time variations in internal space are compatible with present limits on time variations of the fundamental constants. By requiring that the energy density of the particles produced be less than the critical density at the radiation era we set restrictions on two more parameters: namely, the initial time of application of the semiclassical approach and the relative sizes between the internal space and the horizon of the ordinary Universe at this time. Whereas the production of massless particles allows a large range of variation to these parameters, the production of massive particles sets severe constraints on them, since, if they are overproduced, their energy density might very soon dominate the Universe and make cosmological dimensional reduction by extradimensional contraction unlikely.

Cosmological term and fundamental physics

A nonvanishing cosmological term in Einstein's equations implies a nonvanishing spacetime curvature even in the absence of any kind of matter. It would, in consequence, affect many of the underlying kinematic tenets of physical theory. The usual commutative spacetime translations of the Poincare group would be replaced by the mixed conformal translations of the de Sitter group, leading to obvious alterations in elementary concepts such as time, energy and momentum. Although negligible at small scales, such modifications may come to have important consequences both in the large and for the inflationary picture of the early Universe. A qualitative discussion is presented, which suggests deep changes in Hamiltonian, Quantum and Statistical Mechanics. In the primeval universe as described by the standard cosmological model, in particular, the equations of state of the matter sources could be quite different from those usually introduced.

Towards a full cosmological exploitation of cosmic voids

A stately fraction of the Universe volume is dominated by almost empty space. Alongside the luminous filamentary structures that make it up, there are vast and smooth regions that have remained outside the Cosmology spotlight during the past decades: cosmic voids. Although essentially devoid of matter, voids enclose fundamental information about the cosmological framework and have gradually become an effective and competitive cosmological probe. In this Thesis work we present fundamental results about the cosmological exploitation of voids. We focused on the number density of voids as a function of their radius, known as void size function, developing an effective pipeline for its cosmological usage. We proposed a new parametrisation of the most used theoretical void size function to model voids identified in the distribution of biased tracers (i.e. dark matter haloes, galaxies and galaxy clusters), a step of fundamental importance to extend the analysis to real data surveys. We then applied our built methodology to study voids in alternative cosmological scenarios. Firstly we exploited voids with the aim of breaking the degeneracies between cosmological scenarios characterised by modified gravity and the inclusion of massive neutrinos. Secondly we analysed voids in the perspective of the Euclid survey, focusing on the void abundance constraining power on dynamical dark energy models with massive neutrinos. Moreover we explored other void statistics like void profiles and clustering (i.e. the void-galaxy and the void-void correlation), providing cosmological forecasts for the Euclid mission. We finally focused on the probe combination, highlighting the incredible potential of the joint analysis of multiple void statistics and of the combination of the void size function with different cosmological probes. Our results show the fundamental role of the void analysis in constraining the fundamental parameters of the cosmological model and pave the way for future studies on this topic.

Exploiting the clustering of cosmic voids as a novel cosmological probe

The investigations of the large-scale structure of our Universe provide us with extremely powerful tools to shed light on some of the open issues of the currently accepted Standard Cosmological Model. Until recently, constraining the cosmological parameters from cosmic voids was almost infeasible, because the amount of data in void catalogues was not enough to ensure statistically relevant samples. The increasingly wide and deep fields in present and upcoming surveys have made the cosmic voids become promising probes, despite the fact that we are not yet provided with a unique and generally accepted definition for them. In this Thesis we address the two-point statistics of cosmic voids, in the very first attempt to model its features with cosmological purposes. To this end, we implement an improved version of the void power spectrum presented by Chan et al. (2014). We have been able to build up an exceptionally robust method to tackle with the void clustering statistics, by proposing a functional form that is entirely based on first principles. We extract our data from a suite of high-resolution N-body simulations both in the LCDM and alternative modified gravity scenarios. To accurately compare the data to the theory, we calibrate the model by accounting for a free parameter in the void radius that enters the theory of void exclusion. We then constrain the cosmological parameters by means of a Bayesian analysis. As far as the modified gravity effects are limited, our model is a reliable method to constrain the main LCDM parameters. By contrast, it cannot be used to model the void clustering in the presence of stronger modification of gravity. In future works, we will further develop our analysis on the void clustering statistics, by testing our model on large and high-resolution simulations and on real data, also addressing the void clustering in the halo distribution. Finally, we also plan to combine these constraints with those of other cosmological probes.

Hubble parameter reconstruction from a principal component analysis: minimizing the bias

Aims. A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Methods. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. Results. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.

Fractional calculus analysis of the cosmic microwave background

Cosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker spacetime in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a nonlocal term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near a zero scale factor (initial singularity), it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from ``nothing'' into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.

Cosmic strings in extra dimensions

The Einstein equations coupled with a cloud of geometric strings for a five-dimensional Bianchi type-I cosmological model are studied. The cosmological consequences of having strings along the fifth dimension are examined. Particular solutions with dynamical compactifications of the extra dimensions and compatibility with expanding three-dimensional spaces are presented.