TY - JOUR

T1 - The 2-loop matter power spectrum and the IR-safe integrand

AU - Carrasco, John Joseph

AU - Foreman, Simon

AU - Green, Daniel

AU - Senatore, Leonardo

PY - 2014/7/1

Y1 - 2014/7/1

N2 - 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 k NL. 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.

AB - 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 k NL. 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.

KW - cosmological perturbation theory

KW - power spectrum

UR - http://www.scopus.com/inward/record.url?scp=84905499036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905499036&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2014/07/056

DO - 10.1088/1475-7516/2014/07/056

M3 - Article

AN - SCOPUS:84905499036

SN - 1475-7516

VL - 2014

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

IS - 7

M1 - 056

ER -