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

TL;DR

The work surveys a broad spectrum of modified gravity theories as frameworks for cosmology, presenting formalism, viability conditions, and reconstruction techniques to model inflation, dark energy, and bouncing cosmologies. It contrasts scalar-field and gravity-only approaches, examines perturbations and observational indices, and analyzes how features such as Type IV singularities and graceful exit can arise or be controlled within these theories. A central theme is the unification of early- and late-time acceleration within a single modified-gravity framework, including mimetic and unimodular extensions, with attention to consistency with Planck/BICEP2 data and solar-system tests. The paper also discusses astrophysical implications and reconstruction methods, aiming to equip researchers with a toolbox to realize diverse cosmological histories in a self-consistent, testable manner.

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.

Figures (8)

• Figure 1: Comparison of the scaled dark energy density $y_H(z)=\frac{\rho_\mathrm{DE}}{\rho_m^{(0)}}$ over z, for $w=0.2$ (left) and $w=0.8$ (right). The red line corresponds to non-collisional matter and the blue one to collisional matter.
• Figure 2: Behavior of the dark energy equation of state parameter $\omega_\mathrm{DE}(z)$ as a function of the redshift $z$, for $w=0.2$ (left plot) and $w=0.8$ (right plot). The red curves correspond to non-collisional matter while the blue curves correspond to collisional matter.
• Figure 3: Comparison of the Hubble parameter $H(z)$ over z for $w=0.8$. The red line corresponds to non-collisional matter while the blue corresponds to collisional matter.
• Figure 4: Comparison of the effective equation of state parameter $\omega_\mathrm{eff}(z)$ over z, for $w=0.2$ (left) and $w=0.8$ (right). The red line corresponds to non-collisional matter while the blue corresponds to collisional matter.
• Figure 5: Plots of the growth factor $f_g(z)=\frac{d \ln \delta}{d \ln a}$, as a function of the redshift $z$, for $k=0.1$Mpc$^{-1}$ and $w=0.8$. The blue curve corresponds to collisional matter and the red curve to non-collisional matter.