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Early dark energy (EDE) offers a particularly interesting theoretical approach to the Hubble tension, albeit one that introduces its own set of challenges, including a new "why then"problem related to the EDE injection time at matter-radiation equality, and a mild worsening of the large-scale structure (LSS) tension. Both these challenges center on the properties of dark matter, which becomes the dominant component of the Universe at EDE injection and is also responsible for seeding LSS. Motivated by this, we present the potential of couplings between EDE and dark matter to address these challenges, focusing on a mechanism similar to chameleon dark energy theories, deeming this chameleon early dark energy (CEDE). We present relevant background and perturbation equations and study the dynamics of the case of a quartic scalar potential and an exponential coupling.
Karwal et al. (Sat,) studied this question.