The 2-loop matter power spectrum and the IR-safe integrand

TL;DR

This paper introduces a new IR-safe method for computing the 2-loop matter power spectrum in the Effective Field Theory of Large Scale Structures, improving numerical stability and accuracy for cosmological predictions.

Contribution

The authors develop a novel technique to compute all 2-loop diagrams as a single IR-divergence-free integral, simplifying calculations and enhancing reliability.

Findings

Method produces IR-safe, cutoff-independent results

Applicable to scaling universes with power-law spectra

Method generalizes to higher-loop computations

Abstract

Large scale structure surveys are likely the next leading probe of cosmological information. It is therefore crucial to reliably predict their observables. The Effective Field Theory of Large Scale Structures (EFTofLSS) provides a manifestly convergent perturbation theory for the weakly non-linear regime, where dark matter correlation functions are computed in an expansion of the wavenumber k over the wavenumber associated to the non-linear scale knl. To push the predictions to higher wavenumbers, it is necessary to compute the 2-loop matter power spectrum. For equal-time correlators, exactly as with standard perturturbation theory, there are IR divergences present in each diagram that cancel completely in the final result. We develop a method by which all 2-loop diagrams are computed as one integral, with an integrand that is manifestly free of any IR divergences. This allows us to compute the 2-loop power spectra in a reliable way that is much less numerically challenging than standard techniques. We apply our method to scaling universes where the linear power spectrum is a single power law of k, and where IR divergences can particularly easily interfere with accurate evaluation of loop corrections if not handled carefully. We show that our results are independent of IR cutoff and, after renormalization, of the UV cutoff, and comment how the method presented here naturally generalizes to higher loops.