k-essence f(R) gravity inflation

Abstract

solutions of the slow-roll theory, with regard to the scalar field. After that we employ two different approaches in order to study the phenomenological implications of the k-essence f (R) gravity theory. In the first approach, we choose the functional form of the f (R) gravity, and we investigate how the k-essence term affects the cosmological evolution in terms of the Hubble rate. After that we calculate in detail the slow-roll indices of the inflationary theory at hand, and correspondingly the observational indices. Eventually we investigate the parameter space of the theory and we test the phenomenological validity of the theory. The choice of the functional form of the f (R) gravity is such, so that the vacuum f (R) gravity is not phenomenologically viable, so in effect we investigate whether the k-essence f (R) gravity can be a phenomenologically acceptable theory. In the second approach, 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. As we will demonstrate, in this case too, it is possible to produce a viable inflationary evolution in the context of k-essence f (R) gravity. In addition we examine the conditions under which ghosts can occur in the theory, so we discriminate the ghost-free and phantom cases, and the above considerations are given in terms of these two cases.This paper is organized as follows: In section II we investigate when ghost degrees of freedom can occur in a general k-essence f (R) gravity, and we find the no-ghost constraints on a special class of k-essence f (R) gravity models. In section III we present the essential features of the proposed k-essence f (R) gravity theory, we derive the equations of motion and we investigate how the slow-roll conditions affect the resulting solution of the scalar field. After that we choose the functional form of the f (R) gravity and we calculate the slow-roll indices of the resulting theory. Accordingly we calculate the observational indices and we test the validity of the theory by confronting it with the observational data. In section IV we use another approach, by fixing the Hubble rate, and we investigate which k-essence f (R) gravity can produce such a cosmic evolution. We provide detailed formulas for the slow-roll indices as functions of the e-foldings number, and we calculate the observational indices in the slow-roll approximation. Accordingly, the viability of the theory is tested by confronting it with the observational data. Finally, the conclusions follow in the end of the paper.Before we get to the core of this paper, we will discuss in brief the geometric framework which shall be assumed in the rest of thi...

The phase space of k-Essence f(R) gravity theory

“…Thus combining the present results with those of Ref. [10] which indicated compatibility of k-Essence f (R) gravity theory with the latest Planck data, this makes the theory particularly useful for describing inflationary dynamics. Let us focus in the case of having canonical scalar fields and matter domination cosmology, which is achieved by choosing c 1 = −1 and m = − 9 2 .…”

“…In Ref. [10] such a theoretical framework was given in terms of k-Essence f (R) gravity, and it was demonstrated that a viable inflationary era may be generated.…”

Palatini f(R) Gravity and Variants of k-/Constant Roll/Warm Inflation within Variation of Strong Coupling Scenario

“…The first case corresponds to α >> 1, which makes the scalar field noncanonical per excellence. Many studies were carried out to refine the inflationary scenario within the framework of scalar fields possessing a noncanonical kinetic term [16][17][18][19][20][21][22][23]. In actuality, such kinematically-induced inflationary scenarios go back to the Starobinsky model [24,25] more than four decades ago, which considered a geometrical modification to general relativity in order to explain inflation.…”

Nontrivial black hole solutions inf(R)gravitational theory

“…In the frame of f (R) gravity the dynamical behavior of the matter field and dark energy has been studied [41][42][43][44]. From the viewpoint of cosmology, many researchers have been carried out their studies from different directions [45][46][47][48][49][50][51][52][53][54][55][56][57][58]. A spherically symmetric vacuum BH solution in f (R) gravity has been derived in [59][60][61][62].…”