FLRW-Cosmology in Scalar-Vector-Tensor Theories of Gravity

TL;DR

The paper addresses how FLRW cosmology is shaped in generic metric gravity theories that include higher-curvature terms and extra scalar/vector fields. By proving that any symmetric rank-2 tensor built from the metric, curvature, and homogeneous scalar and vector fields collapses to the form \\mathcal{E}_{\\mu\\nu}=A(t) \, g_{\\mu\\nu} + B(t) \, u_{\\mu} u_{\\nu}, the authors reduce the field equations to an Einstein-like system with an effective perfect-fluid source, enabling a transparent Friedmann-language interpretation. They establish a general theorem (Theorem 2) and its corollary for non-minimally coupled scalar-vector gravity, and illustrate with two explicit 4D regularized Einstein–Gauss–Bonnet models: a scalar-tensor and a vector-tensor theory, where the extra sectors contribute as effective fluids with densities \\rho_{\\phi}, \\rho_{w} and pressures \\p_{\\phi}, \\p_{\\w}. These effective fluids alter the standard cosmological constraints through their impact on the density parameters \\Omega_{i} and the curvature-mixing term, providing a unified framework for analyzing modified gravity cosmologies under FLRW symmetry.

Abstract

We generalize our previous theorem for FLRW spacetime within the framework of generic metric gravity theories. In our earlier work, we demonstrated that, in the absence of matter fields, the field equations of any generic gravity theory reduce to the Einstein field equations with an effective perfect fluid source. In the present study, we extend this analysis by incorporating scalar and vector fields into a generic gravity theory and show that the resulting field equations remain equivalent to the Einstein field equations with a perfect fluid distribution. We further verify our findings by explicitly examining recently developed Einstein-scalar and Einstein-Proca field theories.