Constraints on Interacting Early Dark Energy from a Modified Temperature-Redshift Relation and CMB Acoustic Scales

The Hubble tension, reflecting a persistent discrepancy between early- and late-time determinations of the Hubble constant, continues to motivate extensions of the standard cosmological model The Hubble tension motivates extensions of the standard cosmological model that modify pre-recombination physics. In this work we study an early dark energy scalar field coupled to radiation prior to recombination. The interaction leads to energy exchange between the two components and modifies the standard cosmic microwave background temperature redshift relation. We derive the modified temperature evolution from the background equations and interpret it in terms of effective photon non-conservation. We also study linear scalar perturbations in the tight-coupling regime relevant for cosmic microwave background acoustic physics. We show that the interaction affects the background evolution without introducing new dynamical degrees of freedom at the perturbation level. The dominant observational effect arises through a shift in the sound horizon at recombination, which modifies the angular acoustic scale. Using the Planck constraint on the acoustic scale we obtain a consistency bound on the coupling strength and show that deviations from the standard temperature redshift relation are tightly constrained.

💡 Research Summary

The paper addresses the persistent Hubble tension by exploring a pre‑recombination modification to the standard cosmological model: an early dark energy (EDE) scalar field that is exponentially coupled to the radiation sector. The interaction introduces a homogeneous energy exchange between the scalar field and photons, altering the usual radiation dilution law and consequently the cosmic microwave background (CMB) temperature–redshift relation.

Starting from the action (S=\int d^4x\sqrt{-g}{R/2 - (\nabla\phi)^2/2 - V(\phi) + e^{-\sigma\phi}\mathcal{L}m}), the authors derive the modified continuity equation for radiation: (\dot\rho\gamma + 4H\rho_\gamma = (4\sigma/3)\dot\phi\rho_\gamma). Integrating yields (\rho_\gamma\propto a^{-4+\epsilon}) with (\epsilon\equiv (4\sigma\phi)/(3\ln a)). Assuming (\epsilon) is approximately constant during the radiation era, the temperature‑redshift law becomes
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