Gravitational Symmetry Breaking, the Higgs and the Cosmos

A non-minimal interaction between scalar fields and the spacetime curvature is a natural and expected occurrence at the high energies characterising the early Universe. For a spectator field, the time-dependence of the Ricci scalar provides a cosmic clock capable of triggering an out-ofequilibrium phase transition as the Universe evolves from inflation to kination. In the present thesis, we explore the cosmological consequences of the so-called Hubble-induced phase transition and its possible observable signatures.

We first discuss the case of a prototypical scalar field non-minimally coupled to curvature during a phase of kination following inflation. Its exponentially-amplified fluctuations lead to copious particle production while also generating a stochastic gravitational-wave background peaked at high frequencies. We perform hundreds of fully-fledged numerical lattice simulations in 3+1 dimensions to obtain a detailed understanding of the non-linear and nonperturbative aspects of the system.

From the numerical data, we compute a set of parametric formulas that encode several key quantities related to the heating stage and the gravitational-wave spectrum, such as typical energy-densities, timescales, heating temperatures, amplitudes and shape of the gravitational-wave spectrum. Second, we examine the case of the non-minimally-coupled Higgs field undergoing a Hubble-induced phase transition.

The negative running of the Higgs selfcoupling leads to the famous vacuum stability problem, which can be avoided by setting a constraint on low-scale particle-physics measurements of the top quark pole mass as well as high-energy cosmological parameters. If stability is assured, the Higgs can undergo a violent process of nonperturbative particle production which heats the post-inflationary Universe into a Standard-Model plasma before big bang nucleosynthesis. A characteristic gravitational-wave signal is associated to the phase transition, which offers a new window into the high-scale behaviour of the Higgs effective potential, including possible new-physics effects.