Abstract
In this work we investigate the inflationary phenomenological implications of a recently developed ghost-free Gauss–Bonnet theory of gravity. The resulting theory can be viewed as a scalar Einstein–Gauss–Bonnet theory of gravity, so by employing the formalism for cosmological perturbations for the latter theory, we calculate the slow-roll indices and the observational indices, and we compare these with the latest observational data. Due to the presence of a freely chosen function in the model, in principle any cosmological evolution can be realized, so we specify the Hubble rate and the freely chosen function and we examine the phenomenology of the model. Specifically we focus on de Sitter, quasi-de Sitter and a cosmological evolution in which the Hubble rate evolves exponentially, with the last two being more realistic choices for describing inflation. As we demonstrate, the ghost-free model can produce inflationary phenomenology compatible with the observational data. We also briefly address the stability of first order scalar and tensor cosmological perturbations, for the exponential Hubble rate, and as we demonstrate, stability is achieved for the same range of values of the free parameters that guarantee the phenomenological viability of the models.
Highlights
40 years ago, three of the major problems in contemporary cosmology, namely the Horizon Problem, the Flatness Problem and the Magnetic-Monopoles Problem, have been given a successful solution in the context of the inflationary scenario
This paper is organized as follows: In Sect. 2 we briefly review the essential features of the ghost free f (G) gravity, in Sect. 3 we present the inflationary dynamics formalism of f (G) gravity which we shall use in the rest of the paper
We have shown in previous sections that a phenomenologically viable cosmological evolution satisfies these constraints if the free parameters are chosen appropriately, so in view of Eq (111) we may conclude that the tensor perturbations are ghost free and stable, at least at first order
Summary
40 years ago, three of the major problems in contemporary cosmology, namely the Horizon Problem, the Flatness Problem and the Magnetic-Monopoles Problem, have been given a successful solution in the context of the inflationary scenario. Such models may include additional curvature terms, namely the f (R) theories, torsional terms namely the teleparallel f (T ) theories, or the Gauss–Bonnet modified gravities f (G) theories, as well as the generalized f (R, G) theories (see [9,10,11,13,14,15,16]). Such theoretical formulations of gravity are able to model both the early-time expansion and the late-time acceleration, see for example [18] It was demonstrated how ghosts may disappear from the Gauss–Bonnet modified gravity theories in general background [19]. We examine the stability of first order scalar and tensor perturbations, for the exponential cosmological evolution, and as we demonstrate these perturbations are stable for the same range of values of the free parameters, for which the phenomenological viability of the model is achieved. The functional form of the Lagrange multiplier is equal to, λ=
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