Universe acceleration in modified gravities: $F(R)$ and $F(T)$ cases

TL;DR

This paper reviews recent advances in modified gravity theories, specifically $F(R)$ and $F(T)$), focusing on cosmological applications, inflation, late-time acceleration, and astrophysical phenomena like neutron stars.

Contribution

It provides a comprehensive overview of the theoretical and cosmological aspects of $F(R)$ and $F(T)$ gravity, including new insights into their applications and properties.

Findings

Unified inflation and late acceleration scenarios in $F(R)$ and $F(T)$ gravity.

Analysis of finite-time future singularities in $F(T)$ gravity within loop quantum cosmology.

Examination of neutron stars and hyperon problems in $F(R)$ gravity.

Abstract

We review recent progress on cosmological issues and theoretical properties of modified gravity theories. In particular, we explicitly explore the conformal transformation, the Starobinsky inflation, and a unified scenario of inflation and late time acceleration in $F(R)$ gravity and $F(T)$ gravity (extended teleparallel gravity). Furthermore, we examine neutron stars and the hyperon problem in $F(R)$ gravity. Moreover, for loop quantum cosmology (LQC), the natures of finite-time future singularities in $F(T)$ gravity are presented. In addition, we investigate $F(T)$ gravity theories from the Kaluza-Klein (KK) and Randall-Sundrum (RS) theories.