• Accepted Paper

CMB signatures of early dark energy-photon interactions: Temperature evolution and acoustic-scale consistency

Yousef Bisabr

Phys. Rev. D - Accepted 21 October, 2026

DOI: https://doi.org/10.1103/s1p6-sp1f

Abstract

The Hubble tension continues to motivate modifications to pre-recombination physics. We investigate an early dark energy (EDE) scalar field that is exponentially coupled to photons before recombination. The interaction modifies radiation dilution and yields a non-standard cosmic microwave background (CMB) temperature–redshift relation T(z)=T0(1+z)1−β. We specify an exponential potential that realizes the assumed radiation-era scaling solution and consistently perturb both the covariant energy-transfer vector and the Klein–Gordon equation. The photon continuity equation acquires a source term proportional to (4σ/3)δϕ′, whereas the photon Euler equation contains no direct momentum-transfer term for the unweighted photon energy–momentum tensor. Within a restricted smooth-field regime, we evaluate the background by direct quadrature and construct illustrative temperature and polarization peak-shift templates. Using the high-precision Planck acoustic scale, we obtain the semi-analytic acoustic-scale consistency estimate |β|≲1.8×10−3. This estimate is not a likelihood constraint; a quantitative analysis requires a full Boltzmann implementation.

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