Cosmological implications from some proposals in Quantum Gravity

Abstract

In this thesis we present the cosmological applications of some proposals from Quantum Gravity. Namely, we will explore classical and quantum cosmological implications of the Generalized Uncertainty Principle (GUP), the Ho\v{r}ava-Lifshitz (HL) theory of gravity and the Swampland Conjectures. Furthermore, we will also present a detailed analysis of Lorentzian Vacuum Transitions in various contexts. First of all, we will present a study of the classical implications of a general form of the GUP to the standard inflationary scenario driven by a scalar field. We will then present the study of the compatibility between the dS swampland conjecture and the Ho\v{r}ava-Lifshitz $F(\bar{R})$ theories. Then we will study the effects of considering a GUP in the variables of the superspace in a model of the Wheeler-DeWitt (WDW) equation in HL gravity. Finally, we will present a general study of the Lorentzian vacuum transitions. We will present a general method to compute the transition probabilities between two minima of a scalar field potential for any model of the superspace that leads to a generic form of the Hamiltonian constraint, by solving the WDW equation with a semiclassical expansion. We will only consider up to first order in this expansion but the method provides enough information to compute the probabilities up to any desired order. We will then apply the method in different scenarios. With these studies we will approach keys aspects of cosmology that are hoped to be solved by quantum gravity, that is we will explore (at a toy model level): the origin of inflation, the viability of the swampland conjectures and a plausible model to avoid the initial singularity. This thesis encompasses six research articles where these results were presented originally.