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: Future dedicated radio interferometers, including HERA and SKA, are very promising tools that aim to study the epoch of reionization and beyond via measurements of the 21 cm signal from neutral hydrogen. Dark matter (DM) annihilations into charged particles change the thermal history of the Universe and, as a consequence, affect the 21 cm signal. Accurately predicting the effect of DM strongly relies on the modeling of annihilations inside halos. In this work, we use up-to-date computations of the energy deposition rates by the products from DM annihilations, a proper treatment of the contribution from DM annihilations in halos, as well as values of the annihilation cross section allowed by the most recent cosmological measurements from the Planck satellite. Given current uncertainties on the description of the astrophysical processes driving the epochs of reionization, X-ray heating and Lyman-alpha pumping, we find that disentangling DM signatures from purely astrophysical effects, related to early-time star formation processes or late-time galaxy X-ray emissions, will be a challenging task. We conclude that only annihilations of DM particles with masses of similar to 100 MeV, could leave an unambiguous imprint on the 21 cm signal and, in particular, on the 21cm power spectrum. This is in contrast to previous, more optimistic results in the literature, which have claimed that strong signatures might also be present even for much higher DM masses. Additional measurements of the 21cm signal at different cosmic epochs will be crucial in order to break the strong parameter degeneracies between DM annihilations and astrophysical effects and undoubtedly single out a DM imprint for masses different from similar to 100 MeV.