Generalized curvature-matter couplings in modified gravity (1407.2013v2)

Abstract: 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 density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.

Generalized Curvature-Matter Couplings in Modified Gravity

The paper "Generalized Curvature-Matter Couplings in Modified Gravity" by Tiberiu Harko and Francisco S.N. Lobo presents a comprehensive review and exploration of modified gravity theories characterized by generalized curvature-matter couplings. This approach extends traditional gravity models by including explicit nonminimal couplings between the curvature of spacetime and the material content, effectively redefining gravitational interactions.

Overview

In this work, the authors review several frameworks where arbitrary functions of curvature interact with the matter Lagrangian density, leading to non-geodesic motion and the presence of additional forces. These interactions are postulated to provide explanations for several cosmological phenomena without invoking dark matter or dark energy as in standard models. The focus is on how these curvature-matter couplings can offer a unified description of cosmic epochs and possibly account for observations such as the flat rotation curves of galaxies.

Main Concepts

1. Modified Gravity Theories: The paper explores extensions of General Relativity (GR) where the Einstein-Hilbert action is generalized to include functions of the scalar curvature $R$ and the matter Lagrangian $L_m$. This class of theories is deemed "higher-order gravity theories."
2. Curvature-Matter Couplings: By introducing nonminimal couplings between spacetime curvature and matter, new dynamics are predicted. The theories propose a relationship where the covariant derivative of the energy-momentum tensor is non-zero, implying deviations from GR and potential violations of the equivalence principle.
3. Phenomenological Implications: Applied to cosmology, these models provide mechanisms to explain dark energy's properties and interactions, as well as the late-time cosmic acceleration observed in the universe. Notably, they suggest alternative explanations for galactic rotation curves that traditionally require dark matter.
4. Dynamic Equations and Observational Ties: The paper outlines the generalized field equations, showing how they differ from both GR and standard $f(R)$ models. Furthermore, it discusses the observational signatures these theories might have, including implications for astrophysical phenomena and constraints from solar system tests.
5. Interaction with Scalar Fields: The addition of scalar fields nonminimally coupled to matter invites rich dynamics similar to those considered in scalar-tensor theories, potentially offering insights into gravitational phenomena at both cosmic and local scales.

Implications and Speculations

These generalized models predict new gravitational effects, notably the appearance of extra forces in systems where matter and curvature are interlinked. The paper highlights how these forces might account for observations typically attributed to dark matter and dark energy, suggesting a reinterpretation of cosmic acceleration and structure formation. The potential for these theories to reproduce observed galactic rotation profiles without dark matter is particularly intriguing, offering a promising area for future astrophysical investigations.

Future Developments

This area of research holds significant potential to expand our understanding of gravity and its role in cosmic evolution. Future studies might focus on refining the models to better match observational data and exploring new computational techniques to simulate their predictions. The integration of these curvature-matter couplings with quantum field theories could also offer deeper insights into the fundamental fabric of spacetime.

In conclusion, the paper provides a thorough theoretical foundation for generalized curvature-matter couplings in modified gravity, positing them as viable alternatives to dark matter and energy paradigms in current cosmological models. As observational techniques advance, these theories could either substantiate or challenge our core understanding of gravity and its manifestations in the universe.