Thesis title: Classical and Quantum Perturbations to the Primordial Universe
In this Ph.D. thesis we analyse both classical and quantum effects relevant for the study of cosmological perturbations. We choose this particular topic because, through the analysis of cosmological perturbations, it is possible to explore a wide range of different physical phenomena. Moreover, they are a central and important piece in the puzzle of the history of the universe.
The most obvious relevance of cosmological perturbations is the study of structure formation and the large scale structure of the universe. In this regard, such perturbations are related to primordial gravitational waves and primordial magnetic fields. Given their dependence on pre-recombination phenomena, they could give us some information on the universe before hydrogen recombination.
Classical perturbations have been widely studied in literature, with the main focus on isotropic cosmological models. While this is usually a good approximation, the presence of a primordial magnetic field causes a coupling between different algebraic modes of the usual decomposition, connecting density perturbations, primordial magnetic fields and primordial gravitational waves. Moreover, the presence of the magnetic field requires the use of an anisotropic cosmological model. While small, these relations are important in the evolution of anisotropic structures. Furthermore, such primordial seeds of the magnetic fields are widely believed to be the origin of the magnetic fields measured today in galaxies. In the first part of this thesis, we analyse these relations, together with the possible effects that a non ideal, i.e. viscous, cosmological fluid could have on the growth of perturbations. We focus our attention to a Bianchi I model, improving the results of some preceding papers.
The second part of the thesis focuses on the semiclassical approximation of quantum gravity. Quantum effects are believed to influence the birth and dynamics of perturbation seeds and, in general, the dynamics of the primordial universe. This way, the mathematical scheme used to represent these effects is a central point in the description of quantum gravity regarding such seeds.
Furthermore, even more care is required to split the WKB action between embedding variables and physical degrees of freedom, and in many models the quantum gravity corrections to the Schrödinger equation violate the unitarity of the system evolution. This decomposition shares some similarities with the Born-Oppenheimer approximation of molecular physics.
We perform a critical analysis of two different ways to apply this decomposition. In particular, we analyse limits and perspectives of the different proposals to solve the non unitarity problem, even comparing expansions in different fundamental physical constants (Planck constant and mass). We find the source of non-unitary effects in a common assumption in the definition of WKB time, and we propose an alternative formulation. Also, we show how the usual assumptions of classicality of the physical quantities must be handled with care, focusing our attention to the implementation of the classical background in the perturbation scheme.
Studies in this research field are very important because they could bind CMB measurements and primordial gravitational waves to quantum gravity, bringing us finally an experimental playground.