Non-Gaussianity in a Matter Bounce

TL;DR

This paper investigates non-Gaussian signatures in a non-singular matter-bounce cosmology as an alternative to inflation. By applying Maldacena's cubic action in a matter-dominated contracting background, it shows that curvature perturbations $\zeta$ grow on super-Hubble scales, yielding an $O(1)$ amplitude for the three-point function with a predominantly local shape accompanied by sizable $\mathcal{O}(\epsilon^2)$ and $\mathcal{O}(\epsilon^3)$ corrections. The predicted negative amplitudes for local, equilateral, and folded templates, together with distinctive corrections to the shape and a specific squeezed-limit behavior, provide observable contrasts with simple slow-roll inflation, potentially measurable by Planck. The methodology generalizes to Ekpyrotic and multi-field scenarios, offering a framework to distinguish contracting-universe models from inflation through non-Gaussianity measurements.

Abstract

A nonsingular bouncing cosmology in which the scales of interest today exit the Hubble radius in a matter-dominated contracting phase yields an alternative to inflation for producing a scale-invariant spectrum of adiabatic cosmological fluctuations. In this paper we identify signatures in the non-Gaussianities of the fluctuations which are specific to this scenario and allow it to be distinguished from the results of inflationary models.

Figures (6)

• Figure 1: The $f_{NL}$ parameter in the Matter Bounce.
• Figure 2: The shape of non-Gaussianity in the Matter Bounce. The vertical axis is the negative of the shape function. This figure shows the contribution of the terms of order $\epsilon$.
• Figure 3: The shape of non-Gaussianity in the Matter Bounce. This figure shows the contribution of the terms of order $\epsilon^2$.
• Figure 4: The shape of non-Gaussianity in the Matter Bounce. This figure shows the contribution of the terms of order $\epsilon^3$.
• Figure 5: The shape of non-Gaussianity in the Matter Bounce. This figure shows the contribution of all terms.