A non inflationary model with scale invariant cosmological perturbations

TL;DR

This paper proposes a quantum cosmological model where a contracting universe bounces and produces nearly scale-invariant perturbations, aligning with observations without inflation, using Bohmian quantum solutions.

Contribution

It introduces a non-inflationary bouncing universe model with quantum effects that naturally generate scale-invariant perturbations during contraction.

Findings

Produces a nearly scale-invariant spectrum with a slight blue tilt.

Determines the equation of state parameter to be less than approximately 8×10^{-4}.

Estimates the bounce size to be around 10^3 Planck lengths.

Abstract

We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-de Witt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum ($n_{_\mathrm{S}}-1>0$). Taking into account the spectral index constraint as well as the CMB normalization measure yields an equation of state that should be less than $\omega\lesssim 8\times 10^{-4}$, implying $n_{_\mathrm{S}}-1 \sim \mathcal{O}(10^{-4})$, and that the characteristic size of the Universe at the bounce is $L_0 \sim 10^3 \ell_\mathrm{Planck}$, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects.