Interacting Early Dark Energy

Abstract 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. We find that the traditional law of radiation conservation is modified, with ργ∝ a-4+ε, where the parameter ε measures the rate of energy transfer between radiation and EDE. Assuming constant energy transfer, we demonstrate that the scalar field evolves as φ∝ln a, diverging as a approaches zero. Additionally, we demonstrate that the interacting scalar-photon system behaves similarly 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=ρφ/ργ. Our results indicate that r diminishes as the Universe expands, which is essential for a successful EDE model. Our parameter space analysis confirms that the predicted behavior of r during recombination is consistent with current cosmological observations. These insights underscore crucial aspects necessary for any feasible EDE model and present exciting possibilities for resolving the Hubble tension.