Inflation, the Standard Model Higgs and the nature of gravity

This thesis aims to explore aspects of the inflationary and post-inflationary dynamics in the Higgs and Higgs-dilaton inflation models embedded in the framework of Einstein–Cartan gravity. For Higgs inflation, we consider a class of simplified Einstein–Cartan scenarios and employ lattice simulations in 3+1 dimensions to demonstrate that contrary to the metric and Palatini cases, the postinflationary evolution leads to the formation of localized oscillons that produce a stochastic gravitational wave background and induce a period of matter domination. We then perform a complementary analysis to determine their lifetimes.

By approximating the oscillons as spherical, we extract their radial profiles and carry out 1+1-dimensional simulations to establish the rate at which they lose energy. Our findings show that self-interactions at low field values cause the oscillons to emit radiation from their outer layers, significantly reducing their lifetimes compared to what is typically found in the literature.

We then use these results to refine predictions for inflationary observables, as well as for the amplitude and peak frequency of the gravitational wave signal generated by oscillons. For the Higgs–dilaton model, we focus on the separate effects of a non-minimal coupling to the Holst and Nieh–Yan terms. In this scenario, the inflationary observables are determined by the pole structure of the inflaton kinetic term in the Einstein frame and, for a large portion of the parameter space, are related to the field-space curvature.

For the Nieh–Yan case, we find two distinct attractor solutions correlated with the value of one of the dilaton couplings. Besides the known attractor tied to the field-space curvature, we discover a novel attractor induced by a cubic pole in the kinetic term, and whose predictions are consistent with the latest cosmological observations.