Abstract
In this work we study a modified version of f(R) gravity in which higher order kinetic terms of a scalar field are added in the action of vacuum f(R) gravity. This type of theory is a type of k-essence f(R) gravity, and it belongs to the general class of f(R,ϕ,X) theories of gravity, where ϕ is a scalar field and X=12∂μϕ∂μϕ. We focus on the inflationary phenomenology of the model, in the slow-roll approximation, and we investigate whether viable inflationary evolutions can be realized in the context of this theory. We use two approaches, firstly by imposing the slow-roll conditions and by using a non-viable vacuum f(R) gravity. As we demonstrate, the spectral index of the primordial scalar perturbations and the tensor-to-scalar ratio of the resulting theory can be compatible with the latest observational data. In the second approach, we fix the functional form of the Hubble rate as a function of the e-foldings number, and we modify well-known vacuum f(R) gravity reconstruction techniques, in order to find the k-essence f(R) gravity which can realize the given Hubble rate. Accordingly, we calculate the slow-roll indices and the corresponding observational indices, and we also provide general formulas of these quantities in the slow-roll approximation. As we demonstrate, viability can be obtained in this case too, however the result is strongly model dependent. In addition, we discuss when ghosts can occur in the theory, and we investigate under which conditions ghosts can be avoided by using a particular class of models. Finally, we qualitatively discuss the existence of inflationary attractors for the non-slow-roll theory, and we provide hints towards finding general de Sitter attractors for the theory at hand.
Highlights
The primordial era of our Universe is one of the mysteries in modern cosmology that need to be resolved
Before we start discussing the inflationary phenomenology of k-essence f (R) gravity models, we need to investigate when do ghosts occur in the theory
In order to investigate whether ghosts can occur in this theory, we consider the perturbation of the scalar field φ around the background solution φ = φ0, φ = φ0 + φ
Summary
The primordial era of our Universe is one of the mysteries in modern cosmology that need to be resolved. [25–28], so our main aim in this paper is to investigate whether a viable inflationary evolution can be realized in the context of the k-essence f (R) gravity To this end, we investigate how the slow-roll conditions modify the resulting equations of motion, and we derive the solutions of the slow-roll theory, with regard to the scalar field. We fix the functional form of the Hubble rate as a function of the e-foldings number, and we investigate which k-essence f (R) gravity in the slow-roll approximation can produce such a cosmological evolution After this we express the slow-roll indices as functions of the e-foldings number in the slow-roll approximation, and we provide their functional form in detail, and by using the resulting f (R) gravity, we test the validity of the theory by examining the parameter space. Where H(t) is the Hubble rate, H(t) ≡ a (t)/a(t) and the “dot” indicates differentiation with respect to the cosmic time
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