Alberto Salvio

Classically scale-invariant (and perturbative) theories provide a way to understand large hierarchies, as scales are generated through dimensional transmutation. They always lead to first-order phase transitions, since symmetries are radiatively broken, and they generically feature quasiflat potentials, which are suitable for inflation. We construct a simple but fully realistic model of this kind that accounts for all observational evidence of new physics and is remarkably compatible with the most recent constraints on inflationary observables from both the Planck/BICEP/Keck and the Atacama Cosmology Telescope Collaborations. This model illustrates how classical scale invariance generically leads to a nonstandard cosmology in which inflation occurs in two stages: a slow-roll stage and a thermal stage, separated by a radiation-dominated era.

First-order phase transitions produce gravitational waves and primordial black holes. They always occur in field theories where symmetries are radiatively broken and masses are correspondingly generated. These theories predict a period of supercooling: phase transitions become effective at temperatures much smaller than the symmetry-breaking scale. This paper reviews a model-independent approach to study phase transitions in this scenario, which can be adopted if supercooling is strong enough. Perturbative methods can be used to determine the effective action and such model-independent approach allows us to obtain ready-to-use formulas that can be applied to any specific model of this sort.

This paper provides a systematic and complete study of thermal field theory with fermion fields of any kind for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also average angular momentum. This extends a previous study that focused on scalar fields, to all fermion-scalar theories. Both Dirac and Majorana fermions and both Dirac and Majorana masses are covered. A general technique to compute ensemble averages is provided. Path-integral methods are developed to study thermal Green's functions (with an arbitrary number of points) in generic interacting fermion-scalar theories, which cover both the real-time and imaginary-time formalism. These general results are applied to physical situations typical of neutron stars, which are often quickly rotating: The Fermi surface and Fermi momentum, the average energy, number density and angular momentum for degenerate fermions and particle production (such as neutrino production from rotating neutron stars, e.g. pulsars). In particular, it is shown that the neutrino production rate due to the direct URCA (DU) processes grows indefinitely as the angular velocity approaches the inverse linear size of the plasma and, therefore, rotation can significantly increase this rate.

This paper initiates the systematic study of thermal field theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. The focus here is on scalar fields, although some results also apply to fields with arbitrary spins. A general technique to compute ensemble averages is provided. Moreover, path-integral methods are developed to study thermal Green’s functions (with an arbitrary number of points) in generic theories, which cover both the real-time and imaginary-time formalism. It is shown that, while the average angular momentum, like the chemical potentials, does not contribute positively to the Euclidean action, its negative contributions can be compensated by some other contributions that are instead positive, at least in some cases, e.g. when the chemical potentials vanish. As an application of the developed general formalism, it is shown that the production of particles weakly coupled to a rotating plasma can be significantly enhanced compared to the non-rotating case. The Higgs boson production through a portal coupling to a dark sector in the early universe is studied in some detail. The findings of this paper can also be useful, for example, to investigate the physics of rotating stars, ordinary and primordial black holes and more exotic compact objects.

A bstract: It has been suggested that logarithmically enhanced infra-red loop corrections arising in theories with four derivatives correspond to a physical running of couplings, rendering quadratic gravity asymptotically free. We find that these effects depend on the gauge and on the field parameterisation. We compute physical on-shell amplitudes and find genuine infra-red log-enhanced loop corrections, that are process-dependent and cannot be absorbed into running couplings. As a byproduct, we show that the effective action of quadratic gravity at tree level and without matter fields is just Einstein gravity, so positivity bounds are satisfied despite the presence of ghosts.

Theories with radiative symmetry breaking (RSB) lead to first-order phase transitions and the production of gravitational waves as well as primordial black holes if the supercooling period lasted long enough. Here we explain how to efficiently reheat the universe after such period in the above-mentioned class of theories. Two cases are possible, depending on whether the RSB scale is much larger than the electroweak (EW) symmetry breaking scale or not. When it is, the dominant reheating mechanism can be the decays of the field responsible for RSB in the Standard Model (SM) sector. We point out that in a similar way dark matter (DM) can be produced and we analyze in some detail the case of a sterile-neutrino, finding that the full DM abundance is reproduced when this particle is at the 10 ² MeV scale in a well-motivated SM completion. When the RSB scale is not much larger than the EW symmetry breaking scale, we find that efficient reheating always occurs when the energy density of the false vacuum is first entirely transferred to a dark photon and then to SM fermions via dark-photon decays.

The Atacama Cosmology Telescope (ACT) has recently released new measurements and constraints on inflationary observables. In this paper, it is shown that a component of a dynamical affine connection, which is independent of the metric, can easily drive inflation in agreement with these observations. Such geometrical explanation of inflation is analyzed in detail here in the minimal model, including the predictions for the scalar spectral index n s and its running α s , the amplitude of the scalar perturbations, and the tensor-to-scalar ratio r . Furthermore, this minimal model is shown to provide an inflationary attractor: arbitrary initial values of the kinetic energy density are dynamically attracted down to negligible values compared to the potential energy density in homogeneous and isotropic metrics. Also, the role of the Higgs boson during and after inflation is briefly discussed.

We study in detail the production of primordial black holes (PBHs), as well as their mass and initial spin, due to the phase transitions corresponding to radiative symmetry breaking (RSB) and featuring a large supercooling. The latter property allows us to use a model-independent approach. In this context, we demonstrate that the decay rate of the false vacuum grows exponentially with time to a high degree of accuracy, justifying a time dependence commonly assumed in the literature. Our study provides ready-to-use results for determining the abundance, mass and initial spin of PBHs generated in a generic RSB model with large supercooling. We find that PBHs are generically produced in a broad region of the model-independent parameter space. As an application, we identify the subregion that may explain recently reported microlensing anomalies. Additionally, we show that a simple Standard-Model extension, with right-handed neutrinos and gauged B-L featuring RSB, may explain an anomaly of this sort in a region of its parameter space.

This review article provides the basics and discusses some important applications of thermal field theory, namely, the combination of statistical mechanics and relativistic quantum field theory. In the first part, the fundamentals are covered: the density matrix, the corresponding averages, and the treatment of fields of various spin in a medium. The second part is dedicated to the computation of thermal Green’s function for scalars, vectors, and fermions with path-integral methods. These functions play a crucial role in thermal field theory as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should have good knowledge of non-statistical quantum field theory.