Interacting Early Dark Energy

We explore a model of interacting Early Dark Energy (EDE) in which a minimally coupled scalar field, representing the EDE, interacts with the radiation sector through an exponential coupling function in the radiation-dominated era. This framework can be inspired by modified theories of gravity, including $f(R)$ gravity, the Einstein frame representation of Brans-Dicke theory, and chameleon gravity. Our findings reveal that the traditional law of radiation conservation is altered to $\rho_{\gamma}\propto a^{-4+\epsilon}$, where the parameter $\epsilon$ measures the rate of energy transfer between radiation and EDE. Assuming a constant energy transfer, we show that the scalar field behaves as $\phi\propto\ln a$, indicating that $\phi$ diverges as $a$ approaches zero. Additionally, we demonstrate that the interacting scalar-photon system behaves similar to an effective cosmological constant in the early stages of evolution of the Universe. Moreover, by solving the conservation equation associated with the scalar field, we derive an analytical expression for the ratio $r=\rho_{\phi}/\rho_{\gamma}$. Our results indicate that $r$ diminishes as the Universe expands, which is essential for a successful EDE model. Our investigation into the parameter space confirms that the expected behavior of $r$ during recombination aligns with contemporary cosmological data. These insights underscore crucial aspects necessary for any feasible EDE model and present exciting possibilities for resolving the Hubble tension.