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: Purpose. To estimate Type B uncertainties in absorbed-dose calculations arising from the different implementations in current state-of-the-art Monte Carlo (MC) codes of low-energy photon cross-sections (<200 keV). Methods. MC simulations are carried out using three codes widely used in the low-energy domain: PENELOPE-2018, EGSnrc, and MCNP. Three dosimetry-relevant quantities are considered: mass energy-absorption coefficients for water, air, graphite, and their respective ratios; absorbed dose; and photon-fluence spectra. The absorbed dose and the photon-fluence spectra are scored in a spherical water phantom of 15 cm radius. Benchmark simulations using similar cross-sections have been performed. The differences observed between these quantities when different cross-sections are considered are taken to be a good estimator for the corresponding Type B uncertainties. Results. A conservative Type B uncertainty for the absorbed dose (k = 2) of 1.2%-1.7% (<50 keV), 0.6%-1.2% (50-100 keV), and 0.3% (100-200 keV) is estimated. The photon-fluence spectrum does not present clinically relevant differences that merit considering additional Type B uncertainties except for energies below 25 keV, where a Type B uncertainty of 0.5% is obtained. Below 30 keV, mass energy-absorption coefficients show Type B uncertainties (k = 2) of about 1.5% (water and air), and 2% (graphite), diminishing in all materials for larger energies and reaching values about 1% (40-50 keV) and 0.5% (50-75 keV). With respect to their ratios, the only significant Type B uncertainties are observed in the case of the water-to-graphite ratio for energies below 30 keV, being about 0.7% (k = 2). Conclusions. In contrast with the intermediate (about 500 keV) or high (about 1 MeV) energy domains, Type B uncertainties due to the different cross-sections implementation cannot be considered subdominant with respect to Type A uncertainties or even to other sources of Type B uncertainties (tally volume averaging, manufacturing tolerances, etc). Therefore, the values reported here should be accommodated within the uncertainty budget in low-energy photon dosimetry studies.

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.