Renormalized Newtonian Cosmic Evolution with Primordial Non-Gaussianity

TL;DR

The paper develops a field-theoretic, path-integral framework for Newtonian cosmological perturbation theory with primordial non-Gaussian initial conditions and extends the Matarese-Pietroni renormalization group method to derive a closed-form nonlinear propagator. It shows how non-Gaussianity, via the initial power spectrum and bispectrum, modulates the memory of initial conditions, with positive skewness advancing nonlinearity and negative skewness delaying it. The resulting propagator, $G_{ab}(k;\eta_a,\eta_b)$, depends on functionals $F_P[k]$ and $F_B[k]$ of the initial statistics, highlighting potential observational signatures in BAO and the bispectrum. The work suggests 21 cm cosmology as a promising avenue to detect or constrain primordial non-Gaussianity through nonlinear evolution and memory effects.

Abstract

We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affect the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wavenumber. On the other hand, the negative skewness gives the opposite result.

Figures (2)

• Figure 1: Feymann diagrams; an arrow represents the direction of the time.
• Figure 2: RG equation diagram for the propagator.