The reconstruction of f(ϕ)R and mimetic gravity from viable slow-roll inflation

Abstract

In this work, we extend the bottom-up reconstruction framework of F (R) gravity to other modified gravities, and in particular for f (φ)R and mimetic F (R) gravities. We investigate which are the important conditions in order for the method to work, and we study several viable cosmological evolutions, focusing on the inflationary era. Particularly, for the f (φ)R theory case, we specify the functional form of the Hubble rate and of the scalar-to-tensor ratio as a function of the efoldings number and accordingly, the rest of the physical quantities and also the slow-roll and the corresponding observational indices can be calculated. The same method is applied in the mimetic F (R) gravity case, and in both cases we thoroughly analyze the resulting free parameter space, in order to show that the viability of the models presented is guaranteed and secondly that there is a wide range of values of the free parameters for which the viability of the models occurs. In addition, the reconstruction method is also studied in the context of mimetic F (R) = R gravity. As we demonstrate, the resulting theory is viable, and also in this case, only the scalar-to-tensor ratio needs to be specified, since the rest follow from this condition. Finally, we discuss in brief how the reconstruction method could function for other modified gravities.PACS numbers: 04.50. Kd, 95.36.+x, 98.80.Cq,

Viable inflation in scalar-Gauss-Bonnet gravity and reconstruction from observational indices

“…In this section we shall adopt a bottom-up approach in order to realize viable inflationary scenarios in the context of Einstein Gauss-Bonnet gravity. In some previous works [34,35] we have applied this bottom-up approach in various modified gravities, for example f (R) gravity [35] and f (R, φ) gravity [34]. The bottom-up approach has the privilege of starting with a viable theory, and by using the observational indices and specifically the tensor-to-scalar ratio, one seeks for the theory that may realize this phenomenology.…”

Gravitational resonances in mimetic thick branes

“…For more recent works of mimetic gravity in cosmology see Refs. [55][56][57][58][59]. The Friedmann-Robertson-Walker thin brane was considered and the late time cosmic expansion was explained in the favor of observational data, and the initial time cosmological inflation was also produced [60].…”

Slow-roll inflation with exponential potential in scalar-tensor models

“…Some aspects of slow-roll inflation with non-minimal kinetic coupling have been analyzed in [58,59,60,61,62,63]. For a sample papers devoted to the study of slow-roll inflation in the context of Gauss-Bonnet (GB) coupling see [64,65,66,67,68,69,70,71,72,73,74,75,76,77]. This paper is dedicated to the study of the slow-roll inflation in the scalar-tensor model with non-minimal kinetic coupling to the Einstein tensor and coupling of the scalar field to the Gauss-Bonnet 4-dimensional invariant.…”