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We generalize and unify the $f(R,T)$ and $f(R,L_m)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$, of the trace of the energy-momentum tensor $T$, and of the…

We study the effects of the time evolution of the matter-gravity coupling on the luminosity distance, showing it can provide a natural explanation to the apparent Hubble tension. The gravitational coupling evolution induces a modification…

We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is…

We consider f(R,T) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory,…

A Newtonian-like theory inspired by the Brans-Dicke gravitational Lagrangian has been recently proposed in Ref. arXiv:2009.04434(v4). We propose here a new variant of this theory such that the usual Newtonian second law is preserved. The…

We study cosmologies in modified theories of gravity considering Lagrangian density $f(R)$ which is a polynomial function of scalar curvature ($R$) in the Einstein-Hilbert action in vacuum. The field equation obtained from the modified…

Symmetric teleparallel gravity and its $f(Q)$ extensions have emerged as promising alternatives to General Relativity (GR), yet the role of explicit geometry-matter couplings remains largely unexplored. In this work, we address this gap by…

We investigate the cosmological perturbations around FLRW solutions to non- linear massive gravity with a new effective coupling to matter proposed recently. Unlike the case with minimal matter coupling, all five degrees of freedom in the…

We perform a phase space analysis of a non-minimally coupled modified gravity theory with the Lagrangian density of the form $\frac{1}{2} f_{1}(R)+[1+\lambda f_{2}(R)]{{\cal{L}}_{m}}$, where $f_1(R)$ and $f_2(R)$ are arbitrary functions of…

We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small…

In the standard model of cosmology, the background evolution of the Universe can in general be adequately described by general relativity and a uniform and isotropic metric minimally coupled with a collection of perfect fluids. These fluids…

There is a no-go theorem forbidding flat and closed FLRW solutions in massive gravity on a flat reference metric, while open solutions are unstable. Recently it was shown that this no-go theorem can be overcome if at least some matter…

A new class of modified gravity theories with a healthy higher order derivative terms of a function of the matter Lagrangian $f(L_m)$ is considered. Generally the energy momentum tensor is not conserved, leading to the fifth force similar…

We study the evolution of cosmological perturbations in f(G) gravity, where the Lagrangian is the sum of a Ricci scalar R and an arbitrary function f in terms of a Gauss-Bonnet term G. We derive the equations for perturbations assuming…

We discuss recent results on the cosmology of extended theories of gravity formulated in the Palatini approach, i.e., assuming that metric and connection are independent fields. In particular, we focus on the attempts to explain the cosmic…

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian…

A modified theory of general relativity is proposed, where the gravitational constant is replaced by a dynamical variable in space-time. The dynamics of the gravitational coupling is described by a family of parametrized null geodesics,…

We present a phenomenological analysis of current observational constraints on classes of FLRW cosmological models in which the matter side of Einstein's equations includes, in addition to the canonical term, a term proportional to some…

We investigate the late-time cosmological behaviour of scalar-tensor theories with a universal multiplicative coupling between the scalar field and the matter Lagrangian in the matter era. This class of theory encompasses the case of the…

To find more deliberate f(R,T) cosmological solutions, we proceed our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most…