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

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