Cosmological perturbations and stability of nonsingular cosmologies with limiting curvature

Abstract

We revisit nonsingular cosmologies in which the limiting curvature hypothesis is realized. We study the cosmological perturbations of the theory and determine the general criteria for stability. For the simplest model, we find generic Ostrogradski instabilities unless the action contains the Weyl tensor squared with the appropriate coefficient. When considering two specific nonsingular cosmological scenarios (one inflationary and one genesis model), we find ghost and gradient instabilities throughout most of the cosmic evolution. Furthermore, we show that the theory is equivalent to a theory of gravity where the action is a general function of the Ricci and Gauss-Bonnet scalars, and this type of theory is known to suffer from instabilities in anisotropic backgrounds. This leads us to construct a new type of curvature-invariant scalar function. We show that it does not have Ostrogradski instabilities, and it avoids ghost and gradient instabilities for most of the interesting background inflationary and genesis trajectories. We further show that it does not possess additional new degrees of freedom in an anisotropic spacetime. This opens the door for studying stable alternative nonsingular very early Universe cosmologies.

A covariant Lagrangian for stable nonsingular bounce

“…Recent progresses have inspired a wave of looking for stable nonsingular bounce [13][14][15] (see also [16,17]), along the road beyond the cubic Galileon (even the Horndeski theory [18][19][20]). Moreover, the developments of scalar-tensor theory (the GLPV [21] and DHOST theory [22][23][24], the mimetic gravity [25,26]) might also be able to provide us with some chances to implement stable nonsingular cosmologies.…”

Mimetic DBI Inflation in Confrontation with Planck2018 Data

“…Also, to seek for the non-Gaussian features of the primordial perturbations we can use equation (31), (32) and (40). It is important to notice that, although our model is the MDBI model, but the relations (31), (32) and (40) are applicable. This is because the MDBI model is still P (X, φ) one and the differences appear in the definitions of the slow-roll parameters and also the sound speed.…”

“…The authors of [20] have shown that by considering the direct couplings of the higher derivatives of the mimetic field to the curvature of the space-time, it is possible to overcome such instabilities in some ranges of the parameters space. For more papers on the (in)stability issue see [21,22,23,24,25,26,27,28,29,30,30,31,32].…”

Could the black hole singularity be a field singularity?

“…For example, one could propose that (i) singularities are hidden by horizons (Cosmic Censorship Conjecture [10,11]) or that (ii) the theory is modified such that singularities are not allowed, e.g., bouncing universes [12], limiting curvature mechanisms [13][14][15] (for recent studies see Refs. [16,17]), usually implying that the weak energy condition is violated (see Ref. [18] for a review).…”