PSpectRe: A Pseudo-Spectral Code for (P)reheating

TL;DR

PSpectRe is a C++ pseudo-spectral code that efficiently evolves scalar fields in an expanding universe, offering accurate results with fewer points compared to finite differencing methods, and is adaptable for various early-universe cosmology problems.

Contribution

The paper introduces PSpectRe, a novel pseudo-spectral code that improves efficiency and accuracy in simulating post-inflationary scalar field dynamics, with flexible extension capabilities.

Findings

PSpectRe achieves comparable speed to finite differencing codes despite multiple Fourier transforms.

It exhibits excellent energy conservation during simulations.

Reliable results are obtained with fewer spatial points than traditional methods.

Abstract

PSpectRe is a C++ program that uses Fourier-space pseudo-spectral methods to evolve interacting scalar fields in an expanding universe. PSpectRe is optimized for the analysis of parametric resonance in the post-inflationary universe, and provides an alternative to finite differencing codes, such as Defrost and LatticeEasy. PSpectRe has both second- (Velocity-Verlet) and fourth-order (Runge-Kutta) time integrators. Given the same number of spatial points and/or momentum modes, PSpectRe is not significantly slower than finite differencing codes, despite the need for multiple Fourier transforms at each timestep, and exhibits excellent energy conservation. Further, by computing the post-resonance equation of state, we show that in some circumstances PSpectRe obtains reliable results while using substantially fewer points than a finite differencing code. PSpectRe is designed to be easily extended to other problems in early-universe cosmology, including the generation of gravitational waves during phase transitions and pre-inflationary bubble collisions. Specific applications of this code will be pursued in future work.