Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

Strong semiclassical gravity in the universe and the laboratory

Three published papers are resumed in this thesis. Different aspects of the semiclassical theory of gravity are discussed. In chapter 1 we find a new perturbative (yet analytical) solution to the unsolved problem of the metric junction between two Friedmann-Robertson-Walker using Israel's formalism. The case of an expanding radiation core inside an expanding or collapsing dust exterior is treated. This model can be useful in the "landscape" cosmology in string theory or for treating new gravastar configurations. In chapter 2 we investigate the possible use of the Kodama vector field as a substitute for the Killing vector field. In particular we find the response function of an Unruh detector following an (accelerated) Kodama trajectory. The detector has finite extension and backreaction is considered. In chapter 3 we study the possible creation of microscopic black holes at LHC in the brane world model. It is found that the black hole tidal charge has a fundamental role in preventing the formation of the horizon.

On the GKP Vacuum in Gauge/Gravity Correspondences

Within the framework of the AdS5/CFT4 correspondence, the GKP string living on a AdS5 x S5 background finds a counterpart in the anti-ferromagnetic vacuum state for the spin chain, fruitfully employed to investigate the dual N=4 SYM superconformal gauge theory. The thesis mainly deals with the excitations over such a vacuum: dispersion relations and scattering matrices are computed, moreover a set of Asymptotic Bethe Ansatz equations is formulated. Furthermore, the survey of the GKP vacuum within the AdS4/CFT3 duality between a string theory on AdS4 x CP 3 and N=6 Chern-Simons reveals intriguing connections relating the latter to N=4 SYM, in a peculiar high spin limit.