An effective fluid description of scalar-vector-tensor theories under the sub-horizon and quasi-static approximations

Abstract

We consider scalar-vector-tensor (SVT) theories with second-order equations of motion and tensor propagation speed equivalent to the speed of light. Under the sub-horizon and the quasi-static approximations we find analytical formulae for an effective dark energy fluid, i.e., sound speed, anisotropic stress as well as energy density and pressure. We took advantage of our general, analytical fluid description and showed that it is possible to design SVT cosmological models which are degenerate with $\Lambda$CDM at the background level while having gravity strength $G_{\rm eff}<G_{\rm N}$ at late-times as well as non-vanishing dark energy perturbations. We implemented SVT designer models in the widely used Boltzmann solver CLASS thus making it possible to test SVT models against astrophysical observations. Our effective fluid approach to SVT models reveals non trivial behaviour in the sound speed and the anisotropic stress well worth an investigation in light of current discrepancies in cosmological parameters such as $H_0$ and $\sigma_8$.