Efficient implementation of the Time Renormalization Group

TL;DR

This paper presents a highly efficient implementation of the Time Renormalization Group method, significantly reducing computation time for matter power spectrum calculations, enabling large-scale applications like MCMC.

Contribution

It introduces a variable transformation that simplifies the integral computations in TRG, reducing the time by a factor of 50 and making the method more practical for extensive analyses.

Findings

Computation time decreased by a factor of 50.

Pre-computation of thirteen antiderivatives enables faster evaluations.

The method maintains accuracy while improving efficiency.

Abstract

The Time Renormalization Group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to pre-compute only thirteen antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under control, we find that the computation time for nonlinear corrections to the matter power spectrum decreases by a factor of 50. This opens up the possibility to use of TRG for mass production as in Markov Chain Monte Carlo methods. A Fortran code demonstrating this new algorithm has been made publicly available.