xPert: Computer algebra for metric perturbation theory

TL;DR

xPert is a fast, efficient computer algebra package designed for constructing and manipulating high-order metric perturbation equations around arbitrary backgrounds, leveraging tensor algebra and combinatorial formulas.

Contribution

It introduces a novel tensor algebra package that combines explicit combinatorial formulas with efficient index canonicalization for high-order perturbation calculations.

Findings

Handles perturbation orders n=4 or 5 within seconds

Can reach perturbation order n=10 in under an hour

Demonstrates high efficiency through timing benchmarks

Abstract

We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the n-th order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n=4 or n=5 within seconds, or reach n=10 with timings below 1 hour.