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Although $f(R)$ modification of late time cosmology is successful in explaining present cosmic acceleration, it is difficult to satisfy the fifth-force constraint simultaneously. Even when the fifth-force constraint is satisfied, the…

f(R)-theories of gravity are reviewed in the framework of the matter-antimatter asymmetry in the Universe. The asymmetry is generated by the gravitational coupling of heavy (Majorana) neutrinos with the Ricci scalar curvature. In order that…

The effects of a nonminimally coupled curvature-matter model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. This…

We examine the evolution of universe in $f(R,T)$ gravity where $R$ is the Ricci curvature and $T$ is the trace of energy momentum tensor. We focus on the specific form $f(R,T) = R+f(T)$ and explicitly find out the relation between $f(T)$…

We study cosmological expansion in F(R) gravity using the trace of the field equations. High frequency oscillations in the Ricci scalar, whose amplitude increase as one evolves backward in time, have been predicted in recent works. We show…

We investigate the radial behavior of galactic rotation curves by a Fourth Order Gravity adding also the Dark Matter component. The Fourth Order Gravity is a Lagrangian containing the Ricci scalar, the Ricci and Riemann tensor, but the…

Here we analysed a particular type of $F(R)$ gravity, the so-called exponential gravity which includes an exponential function of the Ricci scalar in the action. Such term represents a correction to the usual Hilbert-Einstein action. By…

We study finite-time future singularities in $\mathcal{F}(R,G)$-gravity, where $R$ and $G$ are the Ricci scalar and the Gauss-Bonnet invariant, respectively. In particular, we reconstruct the $F(G)$-gravity and $\mathcal{F}(R,G)$-gravity…

The Higher Order Theories of Gravity - $f(R, R_{\alpha\beta}R^{\alpha\beta})$ - theory, where $R$ is the Ricci scalar, $R_{\alpha\beta}$ is the Ricci tensor and $f$ is any analytic function - have recently attracted a lot of interest as…

With the non-metricity scalar $Q$ as the functional argument, several $f(Q)$ gravity models are found to be proposed which are perfectly able to mimic the late-time accelerated expansion as pointed out by the type Ia supernovae…

In this work we construct a formalism that can reveal the general characteristics of classes of viable $F(R)$ inflationary theories. The assumptions we make is that the slow-roll era occurs, and that the de Sitter scalaron mass $m^2(R)$ of…

Recently there has been a proposal for modified gravitational f(R) actions which include a direct coupling between the matter action and the Ricci scalar, R. Of particular interest is the specific case where both the action and the coupling…

We consider the Palatini formulation of $f(R,T)$ gravity theory, in which a nonminimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as…

We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go…

A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local…

Extensions of the gravity theory in order to obtain traceless field equations have been widely considered in the literature. The leading example of such class of theories is the unimodular gravity, but there are other possibilities like the…

Ricci scalar is the key ingredient of non-Newtonian theory of gravity, where space-time geometry has a crucial role. Normally, it is supposed to be a geometrical field, but interestingly it also behaves like a physical field. Thus it plays…

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the…

The issues of quintessence and cosmic acceleration can be discussed in the framework of $F(R, {\cal G})$ theories of gravity where $R$ is the Ricci curvature scalar and ${\cal G}$ is the Gauss-Bonnet topological invariant. It is possible to…

We propose the study of constant-roll inflation in $F(R)$ gravity. We use two different approaches, one that relates an $F(R)$ gravity to well known scalar models of constant-roll and a second that examines directly the constant-roll…