Abstract: We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(delta t(2)) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(delta t(4)) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(delta t(10)) We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of 'self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(delta t(2)) up to O(delta t(10)) For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when 'self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2) x U(1). We note that the present manuscript is meant to be part of the theoretical basis for the code CosmoLattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosrnolattice.net.

Abstract: We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types of non-singular cosmologies, namely bouncing and asymptotically Minkowski solutions, from a perspective that makes their features more apparent. We study in detail the propagation of gravitational waves near these non-singular solutions and carefully discuss the origin and severity of the instabilities and strong coupling problems that appear. We also investigate the role of the adiabatic sound speed of the matter sector in the regularisation of the gravitational waves evolution. We extend our analysis to more general Born-Infeld inspired theories where analogous solutions are found. As a general conclusion, we obtain that the bouncing solutions are generally more prone to instabilities, while the asymptotically Minkowski solutions can be rendered stable, making them appealing models for the early universe.

Abstract: The evolution of the universe prior to Big Bang Nucleosynthesis could have gone through a phase of early matter domination which enhanced the growth of small-scale dark matter structure. If this period was long enough, self-gravitating objects formed prior to reheating. We study the evolution of these dense early halos through reheating. At the end of early matter domination, the early halos undergo rapid expansion and eventually eject their matter. We find that this process washes out structure on scales much larger than naively expected from the size of the original halos. We compute the density profiles of the early halo remnants and use them to construct late-time power spectra that include these non-linear effects. We evolve the resulting power spectrum to estimate the properties of microhalos that would form after matter-radiation equality. Surprisingly, cosmologies with a short period of early matter domination lead to an earlier onset of microhalo formation compared to those with a long period. In either case, dark matter structure formation begins much earlier than in the standard cosmology, with most dark matter bound in microhalos in the late universe.

Abstract: Asymmetric Dark Matter (ADM) models invoke a particle-antiparticle asymmetry, similar to the one observed in the Baryon sector, to account for the Dark Matter (DM) abundance. Both asymmetries are usually generated by the same mechanism and generally related, thus predicting DM masses around 5 GeV in order to obtain the correct density. The main challenge for successful models is to ensure efficient annihilation of the thermally produced symmetric component of such a light DM candidate without violating constraints from collider or direct searches. A common way to overcome this involves a light mediator, into which DM can efficiently annihilate and which subsequently decays into Standard Model particles. Here we explore the scenario where the light mediator decays instead into lighter degrees of freedom in the dark sector that act as radiation in the early Universe. While this assumption makes indirect DM searches challenging, it leads to signals of extra radiation at BBN and CMB. Under certain conditions, precise measurements of the number of relativistic species, such as those expected from the Planck satellite, can provide information on the structure of the dark sector. We also discuss the constraints of the interactions between DM and Dark Radiation from their imprint in the matter power spectrum.

Abstract: In the framework of a 3+1 scheme with an additional inert state, we consider the thermalisation of sterile neutrinos in the early Universe taking into account the full 4 x 4 mixing matrix. The evolution of the neutrino energy distributions is found solving the momentum-dependent kinetic equations with full diagonal collision terms, as in previous analyses of flavour neutrino decoupling in the standard case. The degree of thermalisation of the sterile state is shown in terms of the effective number of neutrinos, N-eff, and its dependence on the three additional mixing angles (theta(14), theta(24), theta(34)) and on the squared mass difference Delta m(41)(2) is discussed. Our results are relevant for fixing the contribution of a fourth light neutrino species to the cosmological energy density, whose value is very well constrained by the final Planck analysis. For the preferred region of active-sterile mixing parameters from short-baseline neutrino experiments, we find that the fourth state is fully thermalised (N-eff similar or equal to 4).