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LATTICEEASY: A Program for Lattice Simulations of Scalar Fields in an Expanding Universe

Gary Felder, Igor Tkachev

TL;DR

The paper introduces LATTICEEASY, a C++ lattice code for simulating nonlinear scalar-field dynamics in an expanding universe, with a focus on reheating and thermalization after inflation. It explains the numerical approach, including a staggered leapfrog integrator and rescaled variables to remove first-derivative terms, and shows how potentials are encoded via model headers with run settings in parameters.h. The software supports various expansion schemes (no expansion, fixed power-law, or self-consistent Friedmann evolution) and provides rich outputs such as means, spectra, energy densities, and histograms in ASCII form, with plotting notebooks available. It also discusses planned future extensions to include metric perturbations, gauge fields, and possibly fermions, underscoring the role of flexible lattice tools in exploring early-universe physics.

Abstract

We describe a C++ program that we have written and made available for calculating the evolution of interacting scalar fields in an expanding universe. The program is particularly useful for the study of reheating and thermalization after inflation. The program and its full documentation are available on the Web at http://physics.stanford.edu/gfelder/latticeeasy/ . In this paper we provide a brief overview of what the program does and what it is useful for.

LATTICEEASY: A Program for Lattice Simulations of Scalar Fields in an Expanding Universe

TL;DR

The paper introduces LATTICEEASY, a C++ lattice code for simulating nonlinear scalar-field dynamics in an expanding universe, with a focus on reheating and thermalization after inflation. It explains the numerical approach, including a staggered leapfrog integrator and rescaled variables to remove first-derivative terms, and shows how potentials are encoded via model headers with run settings in parameters.h. The software supports various expansion schemes (no expansion, fixed power-law, or self-consistent Friedmann evolution) and provides rich outputs such as means, spectra, energy densities, and histograms in ASCII form, with plotting notebooks available. It also discusses planned future extensions to include metric perturbations, gauge fields, and possibly fermions, underscoring the role of flexible lattice tools in exploring early-universe physics.

Abstract

We describe a C++ program that we have written and made available for calculating the evolution of interacting scalar fields in an expanding universe. The program is particularly useful for the study of reheating and thermalization after inflation. The program and its full documentation are available on the Web at http://physics.stanford.edu/gfelder/latticeeasy/ . In this paper we provide a brief overview of what the program does and what it is useful for.

Paper Structure

This paper contains 6 sections, 7 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Overview
  3. Equations
  4. Evolution Equations
  5. Initial Conditions
  6. Conclusions

Figures (2)

  • Figure 1: The power spectrum of the field $\chi$ in the model $V={1 \over 4} \lambda \phi^4 + {1 \over 2} g^2 \phi^2 \chi^2$. The spectra rise over time as fluctuations of the field are produced. Initially the production occurs in resonant peaks but these are quickly smoothed out.
  • Figure 2: Two-dimensional histogram of the fields $\sigma_R$ and $\sigma_I$ in the SUSY F-Term hybrid inflation model $V = 4 \lambda \vert\phi\vert^2 \left(\vert\sigma\vert^2 + \vert\bar{\sigma}\vert^2\right) + 4 \lambda \vert\bar{\sigma} \sigma - v^2 \vert^2$. The complex field $\sigma$ has fallen down to the minimum of its potential at $\vert\sigma\vert=v$.