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

## TL;DR

This review comprehensively covers modified gravity theories like $F(R)$, $F( ext{G})$, and $F(T)$, discussing their formalism, cosmological applications including inflation, bouncing models, late-time acceleration, and astrophysical solutions, aiming to provide a complete "toolbox" for these theories.

## Contribution

It systematically compiles and explains various modified gravity theories and their applications in cosmology, emphasizing their viability and potential to unify inflation and dark energy.

## Key findings

- Modified gravity theories can produce viable inflationary scenarios.
- These theories can describe bouncing cosmologies.
- They offer a unified framework for inflation and dark energy.

## 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 $F(R)$, $F(\mathcal{G})$ 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.