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.

18 pages, 15 figures, published version

References in corpus (31)

• Healthy theories beyond Horndeski
• Exploring gravitational theories beyond Horndeski
• Towards a Nonsingular Bouncing Cosmology
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Notes on non-singular models of black holes
• Galilean Genesis: an alternative to inflation
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Cosmology with Mimetic Matter
• The Nature of Primordial Fluctuations from Anisotropic Inflation
• Unifying framework for scalar-tensor theories of gravity
• Effective Description of Higher-Order Scalar-Tensor Theories
• The Effective Field Theory of nonsingular cosmology
• Nonsingular Black Hole
• Hamiltonian analysis of spatially covariant gravity
• Matter creation in a nonsingular bouncing cosmology
• Resolving Cosmological Singularities
• Stability of Geodesically Complete Cosmologies
• Subluminal Galilean Genesis
• Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity
• The Effective Field Theory of nonsingular cosmology: II
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Instabilities in Mimetic Matter Perturbations
• Inevitable ghost and the degrees of freedom in f(R,G) gravity
• Higher Derivative Field Theories: Degeneracy Conditions and Classes
• Generalized multi-Galileons, covariantized new terms, and the no-go theorem for non-singular cosmologies
• Inflation from Minkowski Space
• Generalized Galilean Genesis
• Observational signatures of the theories beyond Horndeski
• Canonical Analysis of Inhomogeneous Dark Energy Model and Theory of Limiting Curvature
• On the canonical structure of general relativity with a limiting curvature and its relation to loop quantum gravity
• Resolving the Ostrogradsky Ghost Problem for a Class of Scalar-tensor Theories

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