Cosmic propagators at two-loop order

TL;DR

This paper analyzes two-loop order cosmic propagators within perturbation theory, deriving semi-analytical expressions, testing against simulations, and discussing the importance of regularization at small scales for accurate modeling.

Contribution

It extends the interpolation scheme to two-loop order for cosmic propagators, providing semi-analytical forms and highlighting the need for small-scale regularization.

Findings

Two-loop corrections improve accuracy for redshifts above 0.5.

Large two-loop corrections at low redshift indicate sensitivity to small-scale modes.

Regularization schemes are necessary for higher order loop corrections.

Abstract

We explore the properties of two-point cosmic propagators when Perturbation Theory (PT) loop corrections are consistently taken into account. We show in particular how the interpolation scheme proposed in arXiv:1112.3895 can be explicitly used up to two-loop order introducing the notion of regular parts for the contributing terms. Extending the one-loop results, we then derive and give semi analytical forms of the two-loop contributions for both the cosmic density and velocity propagators. These results are tested against numerical simulations and shown to significantly improve upon one-loop results for redshifts above 0.5. We found however that at lower redshift two-loop order corrections are too large partly due to a strong sensitivity of those terms to the small scale modes. We show that this dependence is expected to be even larger for higher order loop corrections both from theoretical investigations and numerical tests, the latter obtained with Monte Carlo evaluations of the three-loop contributions. This makes small-scale regularization schemes necessary for the use of such higher order corrections.