The art of simulating the early Universe. Part II. Non-canonical cases & gravitational waves

TL;DR

This paper extends lattice simulation techniques to non-canonical field theories and gravitational wave dynamics, providing a comprehensive framework for modeling complex early Universe phenomena with new interactions and configurations.

Contribution

It introduces lattice implementations for non-canonical interactions, initial condition setups, and gravitational wave dynamics, expanding simulation capabilities beyond canonical models.

Findings

Developed methods for simulating non-minimal scalar-gravity couplings

Implemented lattice techniques for axion-like particle interactions

Extended scalar field discretization to arbitrary spatial dimensions

Abstract

We present a discussion on lattice techniques for the simulation of non-canonical field theory circumstances, complementing our previous monograph (arXiv:2006.15122) on canonical cases. We begin by reviewing basic aspects of lattice field theory, including symplectic and non-symplectic evolution algorithms. We then introduce lattice implementations of non-canonical interactions, considering scalars with a non-minimal coupling to gravity, $\phi^2R$, non-minimal scalar kinetic theories, $\mathcal{G}_{ab}(\lbrace\phi_c\rbrace)\partial_\mu\phi^a\partial^\mu\phi^b$, and axion-like particle (ALP) interactions with Abelian gauge fields, $\phi F_{\mu\nu}\tilde F^{\mu\nu}$. Next, we discuss methods to set up special field configurations, including the creation of cosmic defect networks towards scaling (e.g. cosmic strings and domain walls), field configurations based on arbitrary power spectra or spatial profiles, and probabilistic methods as required e.g. for thermal configurations. We further extend the notion of non-canonical theories, discussing the discretization of scalar field dynamics in $d + 1$ dimensions, with $d \neq 3$. Unrelated to non-canonical aspects, we also discuss implementation(s) of gravitational wave (GW) dynamics on the lattice. This document represents the theoretical basis for the non-canonical field theory aspects (interactions, initial conditions, dimensionality) and GW dynamics implemented in ${\mathcal C}$osmo${\mathcal L}$attice v2.0, to be released in 2026.