Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution

Abstract

We systematically review some standard issues and also the latest developments of modified gravity in cosmology, emphasizing on inflation, bouncing cosmology and late-time acceleration era. Particularly, we present the formalism of standard modified gravity theory representatives, like F (R), F (G) and F (T ) gravity theories, but also several alternative theoretical proposals which appeared in the literature during the last decade. We emphasize on the formalism developed for these theories and we explain how these theories can be considered as viable descriptions for our Universe. Using these theories, we present how a viable inflationary era can be produced in the context of these theories, with the viability being justified if compatibility with the latest observational data is achieved. Also we demonstrate how bouncing cosmologies can actually be described by these theories. Moreover, we systematically discuss several qualitative features of the dark energy era by using the modified gravity formalism, and also we critically discuss how a unified description of inflation with dark energy era can be described by solely using the modified gravity framework. Finally, we also discuss some astrophysical solutions in the context of modified gravity, and several qualitative features of these solutions. The aim of this review is to gather the different modified gravity techniques and form a virtual modified gravity "toolbox", which will contain all the necessary information on inflation, dark energy and bouncing cosmologies in the context of the various forms of modified gravity.

New black hole solutions in three-dimensional $\mathit{f(R)}$ gravity

“…It is ingredient to mention that f (R) gravity is an amended of Einstein gravity and restores the general relativity in the limiting case f (R) = R and when f (R) = R then the theory becomes different from GR. The action of f (R) theory can be written as [79][80][81][82][83][84][85][86]…”

De Sitter solutions in Einstein-Gauss-Bonnet gravity

“…Models with both the Ricci scalar and the Gauss-Bonnet term multiplied by some functions of the scalar field are natural generalizations of the models with a minimal coupling [25,26,27]. Also, models with a nonlinear function of the Gauss-Bonnet term can be rewritten in the equivalent form that includes a scalar field without kinetic term [28,29,30,31].…”

“…The cosmological models with the Gauss-Bonnet term are motivated by the string theory [30,31,32,33,34,35,36,37] and are actively used for describing of both the early Universe evolution (inflation) [25,26,27,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55] and the current dark energy dominated epoch [28,29,30,31,36,37,56,57,58,59]. Note that both studies of the Universe evolution are characterized by the quasi de Sitter accelerated expansion of the Universe.…”

New Cosmological Solutions of a Nonlocal Gravity Model

“…There is no a priori reason that GR is an exception and should be theory of gravitation from the Planck scale to the universe as a whole. Taking into account all these remarks it follows that general relativity is not a final gravitational theory and that investigation of its extension is needed, e.g., see [5,6,7,8,9,10,11,12] and references therein.…”

“…Since it is not invented so far a new physical principle that could say in which direction extend GR, there are many approaches to its modification (for a review, see [5,6,7,8,9]). One of the current and attractive approaches to general relativity modification is its nonlocal extension, see e.g.…”