We show that the recent detection of a gravitational wave (GW) background reported by various pulsar timing array (PTA) collaborations including NANOGrav-15 yr, PPTA, EPTA/InPTA, and CPTA can be explained in terms of first order phase transitions (FOPTs) from dark sector models (DSM). Specifically, we explore a model for first order phase transitions that involves the Majoron, a Nambu-Goldstone boson that is emerging from the spontaneous symmetry breaking of a $U(1{)}_L$ or $U(1{)}_{B-L}$ symmetry. We show how the predicted GW power spectrum, with a realistic choice of the FOPT parameters, is consistent with $1\text{−}\sigma$ deviations from the estimated parameters of the background detected by the PTA collaborations.

We investigate a (super-)renormalizable and ghost-free theory of gravity, showing that under a natural (exponential) ansatz of the form factor and a suitable truncation it can give rise to the Starobinsky inflationary theory in cosmological frameworks, and thus offering a theoretical justification of its origin. We study the corresponding inflationary evolution and we examine the generation of curvature perturbations, adapting the $f(R)$-like equations in a symmetry-reduced Friedmann-Lema\^\itre-Robertson-Walker metric. Furthermore, we analyze how the ultraviolet regime of a simply renormalizable and unitary theory of gravity is also compatible with the Starobinsky action, and hence we show that such a theory could account for an inflationary phase of the Universe in the ultraviolet regime.

We study the quantization of a linear scalar field, whose symmetries are described by the $\kappa$-Poincaré Hopf algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (Planckian) cutoff for the modes of the field. At the “multiparticle” level the nontrivial coalgebra structure of $\kappa$-Poincaré leads to a deformed bosonization in the construction of Fock space states. These physical states carry energy-momentum charges which are divergenceless and obey a deformed dispersion relation.

We review matter bounce scenarios where the matter content is dark matter and dark energy. These cosmologies predict a nearly scale-invariant power spectrum with a slightly red tilt for scalar perturbations and a small tensor-to-scalar ratio. Importantly, these models predict a positive running of the scalar index, contrary to the predictions of the simplest inflationary and ekpyrotic models, and hence, could potentially be falsified by future observations. We also review how bouncing cosmological space-times can arise in theories where either the Einstein equations are modified or where matter fields that violate the null energy condition are included.

In recent years, Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless, the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We propose here a general strategy of analysis of the effects of modifications of the dispersion relation in Friedmann-Robertson-Walker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled (“preferred-frame scenarios”) and to the alternative possibility of “DSR-relativistic theories,” theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.