Abstract
In scalar-tensor Horndeski theories, nonsingular cosmological models---bounce and genesis---are problematic because of potential ghost and/or gradient instabilities. One way to get around this obstacle is to send the effective Planck mass to zero in the asymptotic past (``strong gravity in the past''). One may suspect that this feature is a signal of a strong coupling problem at early times. However, the classical treatment of the cosmological background is legitimate, provided that the strong coupling energy scale remains at all times much higher than the scale associated with the classical evolution. We construct various models of this sort, namely (i) bouncing Universe which proceeds through inflationary epoch to kination (expansion within general relativity, driven by massless scalar field); (ii) bouncing Universe with kination stage immediately after bounce; (iii) combination of genesis and bounce, with the Universe starting from flat space-time, then contracting and bouncing to the expansion epoch; (iv) ``standard'' genesis evading the strong coupling problem in the past. All these models are stable, and perturbations about the backgrounds are not superluminal.
Highlights
Nonsingular cosmological models—bouncing cosmology and genesis from Minkowski space—are of continuous interest as alternatives to or completions of inflation
Our cosmologies are complete in the sense that at late times the Universe expands in a standard way: at large positive t, the models turn into general relativity with a conventional massless scalar field that drives the expansion
Unlike at contraction and bounce, gravity at inflation and kination is described by conventional general relativity (GR), and the expansion is driven by the scalar field
Summary
Nonsingular cosmological models—bouncing cosmology and genesis from Minkowski space—are of continuous interest as alternatives to or completions of inflation. In this paper we follow yet another route [24], namely, we stick to the Horndeski theory and ensure that the coefficients GT, F T, GS, and F S (“effective Planck masses” squared) in the quadratic actions for perturbations (1) sufficiently rapidly decay as one goes backwards in time to t → −∞, so that the integral in the left-hand side of Eq (2a) is convergent In this way we relax the assumption of the no-go theorem and construct Horndeski models without gradient or ghost instabilities (at the linearized level). Our cosmologies are complete in the sense that at late times the Universe expands in a standard way: at large positive t, the models turn into general relativity with a conventional massless scalar field that drives the expansion This is kination epoch which is assumed to end up with reheating through, say, one of the mechanisms of Refs.
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