A non inflationary model with scale invariant cosmological perturbations

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.

9 pages, 4 figures

References in corpus (1)

• Scalar and Vector Perturbations in Quantum Cosmological Backgrounds

Cited by in corpus (10)

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• Cosmology without inflation
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• An Inflationary Non-singular Quantum Cosmological Model
• K-Bounce
• On the Transfer of Adiabatic Fluctuations through a Nonsingular Cosmological Bounce
• Cosmic acceleration from interaction of ordinary fluids
• Large classical universes emerging from quantum cosmology