Unified dark sector and Hubble-tension alleviation in scalar–vector–tensor gravity

We investigate a scalar–vector–tensor theory in which matter is minimally coupled to a Jordan-frame metric \(\tilde{g}_{\mu \nu }=(1+\Xi )g_{\mu \nu }\), while a massive vector sector interacts with the baryonic current. We show that the conformal scalar coupling modifies the physical expansion rate measured by matter observers, leading to an enhancement of the Hubble constant inferred at low redshift. We stress, however, that the Hubble rate is not a conformal invariant, whereas the acoustic angular scale \(\theta _s\) is, and we derive the exact integral condition that the scalar field evolution must satisfy. We show that a single-signed scalar velocity cannot satisfy it, and we construct instead a two-epoch phenomenological evolution which matches \(\theta _s\) exactly while retaining the late-time enhancement, at the cost of a small pre-recombination shift of the effective gravitational coupling. We stress that the scalar is not separately conserved, and that retaining the scalar–matter energy exchange in its continuity equation supplies a further restriction: positivity of the scalar energy density bounds the early component to \(z_E\lesssim 13\). Notably, the recombination temperature is unmodified, since particle masses are constant in the Jordan frame, only the expansion rate at that epoch being altered. The scalar potential naturally acts as a dynamical dark-energy sector, while the vector sector provides two distinct contributions. The temporal component, determined algebraically by the baryon current, yields an apparent matter-like term in the background expansion that is not a true fluid but rather a manifestation of the interaction energy. The propagating spatial modes, on the other hand, form a vector condensate that behaves as a collisionless pressureless component and can play the cosmological role of cold dark matter. Hence, the framework connects scalar dynamics, effective dark-energy evolution, and the \(H_0\) tension within a single setup. Finally, local gravitational constraints require a chameleon-type screening mechanism, whose efficiency we discuss critically.