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

TL;DR

This paper proves that in FLRW spacetimes, a broad class of scalar-vector-tensor gravity theories simplify to Einstein-like equations with an effective perfect fluid, highlighting the universality of FLRW metrics.

Contribution

The authors extend previous results to show that FLRW metrics lead to Einstein-like equations in general scalar-vector-tensor theories, regardless of the specific theory form.

Findings

FLRW metrics yield Einstein equations with an effective perfect fluid in broad scalar-vector-tensor theories.

The tensorial structure of the field equations is determined solely by FLRW symmetry, independent of the specific gravity theory.

The cosmological dynamics depend on the theory, despite the universal form of the equations.

Abstract

We generalize our previous theorem for FLRW spacetimes within the framework of generic metric gravity theories. In earlier work, we proved that, in the absence of matter fields, the field equations of any metric gravity theory constructed from the curvature tensor and its covariant derivatives reduce in FLRW spacetime to the Einstein equations with an effective perfect-fluid source. In the present work, we extend this result to a broad class of scalar-vector-tensor theories in which the gravitational action contains arbitrary scalar and vector fields together with their covariant derivatives at any order. We prove that, under the symmetry conditions imposed by FLRW geometry, the metric field equations necessarily take the Einstein form with an effective perfect-fluid source, supplemented by the corresponding scalar and vector field equations. This result shows that FLRW metrics belong to the class of universal metrics: the tensorial structure of the gravitational field equations is solely fixed by the symmetry of the FLRW spacetime and is independent of the specific form of the gravitation theory, while the resulting cosmological dynamics remains theory dependent. We illustrate our theorem using recently proposed Einstein-scalar and Einstein-Proca theories.