Metric-affine f(R,T) theories of gravity and their applications

Abstract

We study f(R,T) theories of gravity, where T is the trace of the energy-momentum tensor T_{μν}, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f(R) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the non-conservation of the energy-momentum tensor, which implies non-geodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.

9 pages

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• Hybrid branes from split kinks
• On the dilation current in metric-affine gravity
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• Dynamics of quasi de Sitter and linear combination of exponential models in extended gravity
• Gravitational waves in Palatini gravity for a non-minimal geometry-matter coupling