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.

Multiple stellar populations in globular clusters with photometry and low resolution spectroscopy

Our view of Globular Clusters has deeply changed in the last decade. Modern spectroscopic and photometric data have conclusively established that globulars are neither coeval nor monometallic, reopening the issue of the formation of such systems. Their formation is now schematized as a two-step process, during which the polluted matter from the more massive stars of a first generation gives birth, in the cluster innermost regions, to a second generation of stars with the characteristic signature of fully CNO-processed matter. To date, star-to-star variations in abundances of the light elements (C, N, O, Na) have been observed in stars of all evolutionary phases in all properly studied Galactic globular clusters. Multiple or broad evolutionary sequences have also been observed in nearly all the clusters that have been observed with good signal-to-noise in the appropriate photometric bands. The body of evidence suggests that spreads in light-element abundances can be fairly well traced by photometric indices including near ultraviolet passbands, as CNO abundance variations affect mainly wavelengths shorter than ~400 nm owing to the rise of some NH and CN molecular absorption bands. Here, we exploit this property of near ultraviolet photometry to trace internal chemical variations and combined it with low resolution spectroscopy aimed to derive carbon and nitrogen abundances in order to maximize the information on the multiple populations. This approach has been proven to be very effective in (i) detecting multiple population, (ii) characterizing their global properties (i.e., relative fraction of stars, location in the color-magnitude diagram, spatial distribution, and trends with cluster parameters) and (iii) precisely tagging their chemical properties (i.e., extension of the C-N anticorrelation, bimodalities in the N content).