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This is the user manual for CosmoLattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoLattice incorporates a series of features that makes it very versatile and powerful: $i)$ it is written in C++ fully exploiting the object oriented programming paradigm, with a modular structure and a clear separation between the physics and the technical details, $ii)$ it is MPI-based and uses a discrete Fourier transform parallelized in multiple spatial dimensions, which makes it specially appropriate for probing scenarios with well-separated scales, running very high resolution simulations, or simply very long ones, $iii)$ it introduces its own symbolic language, defining field variables and operations over them, so that one can introduce differential equations and operators in a manner as close as possible to the continuum, $iv)$ it includes a library of numerical algorithms, ranging from $O(\delta t^2)$ to $O(\delta t^{10})$ methods, suitable for simulating global and gauge theories in an expanding grid, including the case of `self-consistent' expansion sourced by the fields themselves. Relevant observables are provided for each algorithm (e.g.~energy densities, field spectra, lattice snapshots) and we note that remarkably all our algorithms for gauge theories always respect the Gauss constraint to machine precision. In this manual we explain how to obtain and run CosmoLattice in a computer (let it be your laptop, desktop or a cluster). We introduce the general structure of the code and describe in detail the basic files that any user needs to handle. We explain how to implement any model characterized by a scalar potential and a set of scalar fields, either singlets or interacting with $U(1)$ and/or $SU(2)$ gauge fields. CosmoLattice is publicly available at www.cosmolattice.net., Comment: 111 pages, 3 figures and O(100) code files. v1.1 is out, with GW!

This is the user manual for CosmoLattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoLattice incorporates a series of features that makes it very versatile and powerful: $i)$ it is written in C++ fully exploiting the object oriented programming paradigm, with a modular structure and a clear separation between the physics and the technical details, $ii)$ it is MPI-based and uses a discrete Fourier transform parallelized in multiple spatial dimensions, which makes it specially appropriate for probing scenarios with well-separated scales, running very high resolution simulations, or simply very long ones, $iii)$ it introduces its own symbolic language, defining field variables and operations over them, so that one can introduce differential equations and operators in a manner as close as possible to the continuum, $iv)$ it includes a library of numerical algorithms, ranging from $O(δt^2)$ to $O(δt^{10})$ methods, suitable for simulating global and gauge theories in an expanding grid, including the case of `self-consistent' expansion sourced by the fields themselves. Relevant observables are provided for each algorithm (e.g.~energy densities, field spectra, lattice snapshots) and we note that remarkably all our algorithms for gauge theories always respect the Gauss constraint to machine precision. In this manual we explain how to obtain and run CosmoLattice in a computer (let it be your laptop, desktop or a cluster). We introduce the general structure of the code and describe in detail the basic files that any user needs to handle. We explain how to implement any model characterized by a scalar potential and a set of scalar fields, either singlets or interacting with $U(1)$ and/or $SU(2)$ gauge fields. CosmoLattice is publicly available at www.cosmolattice.net., 111 pages, 3 figures and O(100) code files. v1.1 is out, with GW!

We study the nonperturbative dynamics of the Standard Model (SM) after inflation, in the regime where the SM is decoupled from (or weakly coupled to) the inflationary sector. We use classical lattice simulations in an expanding box in (3+1) dimensions, modeling the SM gauge interactions with both global and Abelian-Higgs analogue scenarios. We consider different post-inflationary expansion rates. During inflation, the Higgs forms a condensate, which starts oscillating soon after inflation ends. Via nonperturbative effects, the oscillations lead to a fast decay of the Higgs into the SM species, transferring most of the energy into $Z$ and $W^{\pm}$ bosons. All species are initially excited far away from equilibrium, but their interactions lead them into a stationary stage, with exact equipartition among the different energy components. From there on the system eventually reaches equilibrium. We have characterized in detail, in the different expansion histories considered, the evolution of the Higgs and of its dominant decay products, until equipartition is established. We provide a useful mapping between simulations with different parameters, from where we derive a master formula for the Higgs decay time, as a function of the coupling constants, Higgs initial amplitude and postinflationary expansion rate., Comment: Minor changes to match the PRD published version. Modulation of the Higgs amplitude removed for $q > 200$ in Sec. V, due to improving the time resolution in the Higgs equation of motion. Results unaffected

Living reviews in relativity 24(1), 4 (2021). doi:10.1007/s41114-021-00032-5, The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This white paper outlines the challenges and gains expected in gravitational-wave searches at frequencies above the LIGO/Virgo band, with a particular focus on Ultra High-Frequency Gravitational Waves (UHF-GWs), covering the MHz to GHz range. The absence of known astrophysical sources in this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising gravitational sources. We review several detector concepts that have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of the workshop ���Challenges and opportunities of high-frequency gravitational wave detection��� held at ICTP Trieste, Italy in October 2019, that set up the stage for the recently launched Ultra-High-Frequency Gravitational Wave (UHF-GW) initiative., Published by Inst., Potsdam