Gravitational Clustering from Chi^2 Initial Conditions

TL;DR

This paper analyzes χ^2 (dimensional-scaling) primordial non-Gaussian initial conditions and their impact on large-scale structure, focusing on the power spectrum and bispectrum in real and redshift space. Using perturbation theory and 2LPT, it shows that non-Gaussian initial conditions induce strong nonlinear couplings, yielding a bispectrum with amplitudes 2–4 times larger than Gaussian cases and a residual scale dependence after nonlinear evolution. It demonstrates how galaxy biasing can be incorporated via an effective nonlinear bias and that redshift-space distortions modify but do not erase these signatures, making the bispectrum a powerful discriminator of dimensional-scaling non-Gaussianity and a tool to constrain inflationary scenarios. The results provide practical diagnostics for comparing χ^2 models with galaxy surveys through $Q_{123}$, the redshift-space bispectrum, and the velocity divergence spectrum, guiding future observational tests.

Abstract

We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $χ^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from large-scale structure galaxy surveys. Non-Gaussian initial conditions provide additional non-linear couplings otherwise forbidden by symmetry that cause non-linear gravitational corrections to become important at larger scales than in the Gaussian case. In fact, the lack of hierarchical scaling in the initial conditions is partially restored by gravitational evolution at scales $k> 0.1$ h/Mpc. However, the bispectrum shows much larger amplitude and residual scale dependence not present in evolution from Gaussian initial conditions that can be used to test this model against observations. We include the effects of biasing and redshift distortions essential to compare this model with galaxy redshift surveys. We also discuss the effects of primordial non-Gaussianity on the redshift-space power spectrum and show that it changes the shape of the quadrupole to monopole ratio through non-linear corrections to infall velocities.