Abstract
We describe how to reconstruct generalized scalar–tensor gravity (GSTG) theory, which admits exact solutions for a physical type of potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is an a priori specified relation between the Hubble parameter H and a function of a non-minimal coupling F=1+delta F, Hpropto sqrt{F}. Deviations from Einstein gravity delta F induce corresponding deviations of the potential delta V from a constant value and modify the dynamics from a pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such a consideration allows us to substitute the physical potential into the obtained equations and then to calculate the non-minimal coupling function and kinetic term that define the GSTG parameters. With this method, we reconstruct GSTG for the polynomial, exponential, Higgs, Higgs–Starobinsky and Coleman–Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove the correspondence of the obtained solutions to observational data from Planck.
Highlights
We note that the main parameters characterizing the type of cosmological model of the early universe are the potential of a scalar field V (φ), the non-minimal coupling function F(φ), which determines the physical processes that occur at the inflationary stage, and the Hubble parameter H (t) corre
We find that the exponential power-law (EPL)-models based on the generalized scalar–tensor gravity (GSTG) under consideration correspond to observational constraints on the parameters of cosmological perturbation for any m > 0 and we estimated the value of the parameter λ as well
We examined cosmological inflationary models with an EPL expansion of the early universe based on scalar–tensor gravity theories implying a non-minimal coupling of the scalar field and curvature
Summary
One of the first modifications of GR is the scalar–tensor gravity theories [20,21]. This type of modified gravity theories successfully solves the problems of constructing consistent scenarios for the evolution of the early universe and its repeated accelerated expansion. The use of ansatzes makes it possible to obtain exact analytical solutions of the dynamic equations, on the other hand, on the basis of this method it is possible to single out cases that have the correct physical interpretation As example of such an approach, we can mention the models of cosmological inflation with “constant roll” based on GR, f (R)-gravity and scalar–tensor gravity [32,33,34,35]. The physical content of the relation H = λ F in the inflationary models based on GSTG is that the non-minimal coupling of a scalar field and curvature, otherwise the deviations from Einstein gravity, induce the corresponding deviations from a pure exponential expansion and the deviations of its potential from the constant [27].
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