f(R,T) gravity

Abstract: We consider f(R,T) modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function f(R,T), are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,T^{\phi})$ models, where $T^{\phi}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra-acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

• The paper introduces f(R,T) gravity, an extension of f(R) gravity incorporating the trace of the stress-energy tensor into the gravitational Lagrangian.
• It derives the field equations for this generalized theory and explores specific models relevant to cosmology, including the role of scalar fields.
• The framework predicts non-geodesic motion for test particles and derives constraints on the resulting extra acceleration from analyzing Mercury's perihelion precession.

An Overview of f(R,T) Gravity

The paper authored by Tiberiu Harko, Francisco S. N. Lobo, and Shin’ichi Nojiri introduces an extension to the standard theory of general relativity, termed as f(R,T) gravity. This research explores the generalization of f(R) gravity by including the dependence on the trace of the stress-energy tensor, T, alongside the Ricci scalar, R, in the gravitational Lagrangian. The fundamental premise of the study is to determine the implications that arise from considering both R and T, as opposed to traditional models that are solely R-dependent.

Derivation of Field Equations

The paper meticulously derives the gravitational field equations from a variational principle, establishing a framework where the field equations are functions of both geometric and matter components. The strength of this approach lies in its capacity to encompass a diverse range of matter types, thereby broadening the scope of gravitational models that can be theoretically examined.

Specific Models and Scalar Field Implications

The authors explore particular instances of f(R,T) models, emphasizing the important role that scalar fields play in cosmological contexts. They explore the possibility of reconstructing Friedmann-Robertson-Walker (FRW) cosmologies using appropriate choices of the function f(T). By inserting scalar field contributions into the model, the paper examines scenarios relevant to inflation, dark energy, and dark matter frameworks.

Non-Geodesic Motion and Extra-Acceleration

A distinguishing feature of the f(R,T) gravity framework is the non-geodesic motion of test particles, attributed to the non-zero covariant divergence of the stress-energy tensor. The paper derives the equations of motion for these test particles and extends the analysis to explore the Newtonian limit. Furthermore, it establishes a constraint on the magnitude of the additional acceleration stemming from f(R,T) modifications by analyzing the perihelion precession of Mercury.

Constraints from Mercury's Perihelion

One of the notable empirical applications discussed is the derivation of the constraint on extra-acceleration, informed by perihelion precession. The precision of Mercury's orbital parameters provides a useful benchmark to constrain the permissible magnitude of already hypothesized extra-dynamical effects within the Solar System.

Implications and Further Research Directions

The exploration of f(R,T) gravity reveals several potential deviations from general relativity. These deviations have implications for the understanding of cosmic evolution, notably in cosmological models and gravitational wave scenarios. The inclusion of a matter component in the Lagrangian could imply distinct signatures in observations, potentially providing a path to test these generalized theories.

Theoretical and Practical Considerations

Theoretically, f(R,T) gravity presents a rich domain for exploring gravitational phenomena where matter-geometry coupling is significant. Practically, this study lays the groundwork for developing cosmological models that may address unresolved issues like the cosmic acceleration problem without resorting to ad-hoc assumptions or purely exotic matter theories.

As this paper suggests, further investigation is warranted to construct explicit physical models within the f(R,T) framework that align with observable astrophysical phenomena. Establishing observational signatures will be crucial for validating or refuting these theoretical advancements in the landscape of contemporary gravitational physics.