Abstract
As a prospective resolution of the Hubble tension, early dark energy (EDE) suffers from the coincidence problem, why EDE is active just at matter-radiation equality (equivalently why the slope of EDE potential is required to approximately equal to the Hubble parameter at that time). In this paper we present a dark-matter-trapped EDE mechanism, by which the bound on the slope of EDE potential can be relieved. We show how this mechanism can work, and discuss the possibility that after inflation ended EDE can settle down at the initial conditions required by observations.
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