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

TL;DR

This work investigates a pre-recombination coupling between an early dark energy scalar field and radiation, which modifies the CMB temperature-redshift relation to $T(z)=T_0(1-z)^{1-\beta}$ and shifts the comoving sound horizon through changes in the photon-baryon fluid background. The perturbation structure remains unchanged at linear order, with the dominant effect arising from background evolution that alters the sound speed and the acoustic horizon. A semi-analytic analysis against Planck’s measured angular acoustic scale yields a stringent constraint $|\beta|\lesssim 10^{-3}$, indicating that even small non-adiabatic photon evolution is highly restricted. The results place early-time physics—specifically photon energy exchange with an EDE field—within a narrow parameter space, offering a defined route to explore potential resolutions to the Hubble tension while highlighting the power of precise CMB acoustic-scale measurements to probe thermal history modifications.

Abstract

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.

Figures (2)

• Figure 1: CMB temperature–redshift relation in the recombination era. The solid curve shows the standard adiabatic scaling $T(z)=T_0 (1+z)$ while the dashed and dotted curves correspond to the modified evolution induced by EDE–photon coupling with $\beta=+0.001$ and $\beta=-0.001$, respectively. Although the deviation from the standard relation is small, it is systematic and becomes relevant at the epoch of last scattering.
• Figure 2: Ratio of the comoving sound horizon at recombination in the presence of EDE--photon coupling $r_s(\beta)$ to its standard $\Lambda$CDM value as a function of the coupling parameter $\beta$. The result is shown in the small-coupling regime $\beta\ll 1$ where the fractional change in the sound horizon scales linearly with $\beta$. The horizontal dashed line indicates the standard $\Lambda$CDM prediction.