Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution (1705.11098v3)

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.

• The paper introduces modified gravity theories, showing how frameworks like F(R), F(𝒢), and F(T) can model inflation and dark energy dynamics.
• It employs robust mathematical formalism to ensure model stability by avoiding antigravity and ghost issues while matching cosmic data.
• The study explores bouncing cosmologies and unified early and late-time acceleration, offering insights for future observational tests.

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

This paper provides a comprehensive review of modified gravity theories in the context of cosmology, focusing on inflation, bouncing cosmology, and late-time acceleration. The authors systematically present the formalism of standard modified gravity representatives such as $F(R)$, $F(\mathcal{G})$, and $F(T)$ gravities, and discuss how these theories can offer viable descriptions of the Universe. Particular emphasis is placed on the compatibility of these theories with observational data and their potential to describe both inflationary and dark energy eras.

Formalism of Modified Gravity Theories

The paper begins by detailing the mathematical structure of several modified gravity theories. For $F(R)$ gravity, the authors provide useful insights into the effective equation of state parameter and the conditions required to avoid antigravity regions. The authors extend the discussion to include $f(\mathcal{G})$ gravity, highlighting its capability to resolve singularities due to the topological nature of the Gauss-Bonnet term. $F(T)$ gravity is discussed, noting its lack of local Lorentz invariance and its implications for cosmology and astrophysical solutions.

Two other remarkable constructions are mentioned: massive gravity and mimetic gravity. The former involves the introduction of a massive graviton to explain cosmological acceleration without a cosmological constant, while the latter uses a mimetic field to incorporate the conformal degree of freedom into the gravitational action, effectively mimicking dark matter effects.

Unified Description of Cosmological Evolution

An essential aspect of this paper is its focus on attempts to unify early and late-time acceleration within modified gravity theories. The authors delve into various models that promise a seamless explanation from the inflationary phase to present-day cosmic acceleration. Several phenomenological criteria for viable models are outlined, focusing on the stability and avoidance of singularities or ghost degrees of freedom.

Inflationary and Bouncing Cosmologies

The text highlights inflationary dynamics realized within the modified gravity framework. Different versions such as scalar-tensor modifications and higher-order curvature invariant models are explored. A significant portion is devoted to how these theories can describe an inflationary Universe, and under what circumstances they can align with data from the Planck satellite and other observatories. In terms of bouncing cosmologies, the paper addresses how singularity-free cosmic bounces can be achieved by specific configurations of $F(R)$ and alternative gravity theories.

Practical and Theoretical Implications

The practical implications of these theories are profound. By extending General Relativity, modified gravity theories can potentially offer explanations for cosmic observations not easily described by the standard model. In particular, they provide arena for addressing both early Universe phenomena and late-time cosmic acceleration through a unified theoretical framework without appealing to unknown forms of dark energy or inflationary fields.

Future Prospects

Speculation on future developments in the context of modified gravity is briefly touched upon, suggesting these theories might eventually offer predictions that could be tested by future cosmic observations, possibly further restricting or even ruling out some models.

Conclusions

The paper concludes by summarizing the viability of modified gravity theories in the context of inflation and dark energy while recognizing the complexities and unresolved issues that remain, such as the stability of solutions and the precise nature of the dark energy component that causes the observed late-time acceleration.

In all, this review offers a substantial examination of modified gravity theories and cosmology, emphasizing the importance of observational correspondence, theoretical robustness, and the potential unity in describing the universe’s large-scale behavior.