We discuss constraints to some nonminimally (NMC) coupled curvature-matter models of gravity by means of Solar System experiments. First we discuss a NMC gravity model which constitutes a natural extension of 1/R^n gravity to the nonminimally coupled case. Such a NMC gravity model is able to predict the observed accelerated expansion of the Universe. Differently from the f(R)=1/R^n gravity case, which is not compatible with Solar System observations, it turns out that this NMC model is a viable theory of gravity. Then we consider a further NMC gravity model which admits Minkowski spacetime as a background, and we derive the 1/c expansion of the metric. The nonrelativistic limit of the model is not Newtonian, but contains a Yukawa correction. We look for trajectories around a static, spherically symmetric body. Since in NMC gravity the energy-momentum tensor of matter is not conserved, then the trajectories deviate from geodesics. We use the NMC gravity model to compute the perihelion precession of planets and we constrain the parameters of the model from radar observations of Mercury.

We present a novel mechanism for generating a Cosmological Constant and suitably sequestering the vacuum contribution to it, so that the eponymous Cosmological Constant problem is avoided. We do so by resorting to a model endowed with a non-minimal coupling between curvature and matter in an appropriately defined relaxed regime, and show that this shares features with both Unimodular gravity as well as a recent proposal to sequester the vacuum contribution through the use of an external term to the action functional.

A previous work found that a nonminimally coupled theory of gravity can, under appropriate conditions, give rise to an additional contribution to the field equations interpreted as dark matter [1]: in particular, the density of this dark matter component was found to scale as a power of the density of visible matter. However, no explicit solution for the modified field equations was provided, so that a direct computation of the specific density profile followed by visible matter is missing. This question is now addressed: analytical solutions to the modified field equations are derived in the appropriate perturbative regime and characterised, with an emphasis on directly obtaining the visible matter profile in a self-consistent way. We compare with known profiles for visible and dark matter and obtain constraints on the parameters of the model.

The possibility that inflation is driven by a massive vector field with SO(3) global symmetry nonminimally coupled to gravity is presented. Through an appropriate Ansatz for the vector field, the behaviour of the equations of motion is studied through the ensuing dynamical system, focusing on the characterisation of the ensuing fixed points.

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 work expands upon previous results, extending the framework developed there to compute corrections up to order $O(1/{c}^{4})$ of the 00 component of the metric tensor. It is shown that additional contributions arise due to both the nonlinear form ${f}^{1}(R)$ and the nonminimal coupling ${f}^{2}(R)$, including exponential contributions that cannot be expressed as an expansion in powers of $1/r$. Some possible experimental implications are assessed with application to perihelion precession.

We generalize the mechanism for gravitational baryogensis in the context of f(R) theories of gravity, including a nonminimal coupling between curvature and matter. In these models, the baryon asymmetry is generated through an effective coupling between the Ricci scalar curvature and the net baryon current that dynamically breaks Charge conjugation, parity and time reversal (CPT) invariance. We study the combinations of characteristic mass scales and exponents for both nontrivial functions present in the modified action functional and establish the allowed region for these parameters: we find that very small deviations from general relativity are consistent with the observed baryon asymmetry and lead to temperatures compatible with the subsequent formation of the primordial abundances of light elements. In particular, we show the viability of a power-law nonminimal coupling function f(2)(R) similar to R-n with 0 < n similar or equal to 0.078 and determine its characteristic curvature scale.

In this work a new non-minimally coupled model is presented, where a generic function $f(R)$ of the scalar curvature factors the usual Einstein-Hilbert action functional, motivated by relevant results obtained from similar models. Its cosmological dynamics are derived and the possibility of attaining a phase of accelerated expansion is assessed. To further probe the possible implications of the model, a dynamical system formulation is established, and used to assess the scenarios where $f(R)$ assumes a power-law or exponential form.

In this work, we use a dynamical system approach to analyse the viability of $f(R,\mathcal{L})$ candidates for dark energy. We compare these with nonminimal coupled $f(R)$ theories and study the solutions for exponential and power-law forms in order to constraint the allowed range of model parameters.

In this work, we use a dynamical system approach to analyse the viability of f(R,ℒ) candidates for dark energy. We compare these with nonminimal coupled f(R) theories and study the solutions for exponential and power-law forms in order to constraint the allowed range of model parameters.

In this work we explore the viability of nonminimally coupled matter- curvature gravity theories, namely the conditions required for the absence of tachyon instabilities and ghost degrees of freedom. We contrast our finds with recent claims of a pathological behaviour of this class of models, which resorted to, in our view, an incorrect analogy with k-essence.

The bumblebee model of spontaneous Lorentz symmetry breaking is explored in a cosmological context, considering a single nonzero time component for the vector field. The relevant dynamic equations for the evolution of the Universe are derived and their properties and physical significance are studied. We conclude that a late-time de Sitter expansion of the Universe can be replicated, and attempt to constrain the parameter of the potential driving the spontaneous symmetry breaking.

In this work we study how a nonminimal coupling between matter and gravity can modify the structure of a homogeneous spherical body. The physical relevance of the adopted Lagrangian density is ascertained, with results obtained for two different choices of the latter.

In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions, f1(R) and f2(R), of the Ricci scalar curvature R: the former extends the usual linear term found in the Einstein–Hilbert Lagrangian, while the latter is multiplied by the matter Lagrangian density, thus introducing an explicit nonminimal coupling.Based upon a Taylor expansion around R=0 for both functions, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the perturbation of the tt component of the metric tensor is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. It is shown that this effect can be canceled or made arbitrarily small when the characteristic mass scales of the two functions are similar. We conclude that the Starobinsky model for inflation complemented with a generalized preheating mechanism is not experimentally constrained by observations. The geodetic precession effects of the model are also shown to be of no relevance for the constraints.

In this work we study how nonminimally coupled theories of gravity modify the usual Friedmann equation, and develop two methods to treat these. The ambiguity in the form of the Lagrangian density of a perfect fluid is emphasized, and the impact of different dominant matter species is assessed. The cosmological constant problem is also discussed.

We develop a framework for constraining a certain class of theories of nonminimally coupled (NMC) gravity with Solar System observations.

In this work a dynamical system approach to nonminimal coupled f(R) theories is made. The solutions of three distinct models are obtained and their stability and physical interpretation are studied to ascertain their viability as candidates for dark energy. Comparison is drawn with previous works in the context of f(R) and nonminimally coupled models.

In this work we explore the viability of nonminimally coupled matter-curvature gravity theories, namely the conditions required for the absence of tachyon instabilities and ghost degrees of freedom. We contrast our finds with recent claims of a pathological behaviour of this class of models, which resorted to, in our view, an incorrect analogy with k-essence.

In this work the Bumblebee model for spontaneous Lorentz symmetry breaking is considered in the context of spherically symmetric astrophysical bodies. A discussion of the modified equations of motion is presented and constraints on the parameters of the model are perturbatively obtained.

In this contribution we assess the current experimental status of Special and General Relativity. Particular emphasis is put on putative extensions of these theories and on how these could be detected experimentally.