Direct and fast calculation of regularized cosmological power spectrum at two-loop order

Abstract

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory (PT), based on the multi-point propagator expansion. In this approach power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard PT results at low-k. With the help of N -body simulations, we show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent-level in the weakly non-linear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of pre-computed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum cosmic emulator from which a wide variety of cosmological models can be explored. The fortran program with which direct and fast calculations of power spectra can be done, RegPT, is publicly released as part of this paper.

Precision modeling of redshift-space distortions from a multipoint propagator expansion

“…Here, following the same technique as used in Ref. [45], we derive alternative expression for which the term is expanded as the polynomials of µ and f . The detail of derivation is described in Appendices A and B of Ref.…”

“…Thus, for a practical computation of P Kaiser , we just follow the prescription presented in Ref. [45], and use the same technique to calculate each power spectrum contribution at oneand two-loo order. In Appendix A, we give explicit expressions for the power spectra P ab up to the two-loop order.…”

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: signs of neutrino mass in current cosmological data sets

“…We use the linear matter power spectrum as input for the non-linear power spectrum produced via RegPT (Taruya et al 2012) as well as the correction terms summarised in section 6 of Beutler et al (2013). Strictly speaking, RegPT is not designed to include the non-linear clustering contribution of neutrinos.…”

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies

“…Some improvements have recently been achieved on i) beyond the linear regime for the real space power spectrum using perturbation theory schemes. There are several models that attempt to do this task: cosmological standard perturbation theory (see Bernardeau et al 2002 and references therein), Lagrangian perturbation theories (Hivon et al 1995;Matsubara 2008;Carlson, White & Padmanabhan 2009;Okamura, Taruya & Matsubara 2011;Valageas & Nishimichi 2011), time renormalization (Pietroni 2008;Anselmi & Pietroni 2012), Eulerian resumed perturbation theories (Crocce & Scoccimarro 2006;Bernardeau, Crocce & Scoccimarro 2008;Wang & Szalay 2012;Elia et al 2011;Taruya et al 2012;Bernardeau, Crocce & Scoccimarro 2012) and closure theory (Taruya & Hiramatsu 2008). Recent improvements in the galaxy bias model describe accurately how the galaxies trace dark matter, including non-linear and non-local terms (Nishimichi & Taruya 2011;McDonald & Roy 2009;Saito et al 2014) in addition to primordial non-Gaussian terms (Biagetti et al 2014).…”