Disformal interactions in the Dark Sector: From driving Early Dark Energy to confronting cosmological tensions

Abstract: The $\Lambda$CDM model faces significant challenges, including an incomplete understanding of the dark sector and persistent tensions in the Hubble constant and the clustering amplitude. To address these issues, we propose a general disformal coupling between dark energy (DE) and dark matter from a field-theoretic action which can generate a rich variety of interactions including conformal and pure-momentum coupling scenarios. Our analysis reveals that a pure disformal coupling naturally produces a unique interacting Early Dark Sector, wherein the interactions with dark matter suppress the Hubble friction on the DE scalar field leading to a kinetic-driven cosmological constant-like behavior at early times followed by its dilution as $a^{-6}$ and eventually leading to a potential-driven epoch characteristic of late-time dark energy. In contrast to existing Early Dark Energy (EDE) models that rely on finely-tuned potentials, the EDE-like behavior, in our framework, is purely a consequence of the disformal coupling paired with the dilution of dark matter, offering a more fundamental and less ad hoc solution to cosmological tensions. This framework also predicts a suppression of power in the CMB temperature spectrum on large angular scales, offering a potential physical explanation for the observed low-$\ell$ anomaly. By deriving these effects from a fundamental action, our work provides a unified, testable alternative to $\Lambda$CDM that can be constrained by next-generation cosmological surveys and gravitational wave observations.