  Early dark energy is a promising potential resolution of the Hubble tension.
Unfortunately, many models suffer from the need to fine-tune their initial
conditions to ensure that the epoch of early dark energy coincides with
matter-radiation equality. We propose a class of attractive early dark energy
models where this coincidence arises naturally as a saddle point of a dynamical
system that attracts a large volume of phase-space trajectories regardless of
the initial conditions. The system approaches a global dark energy attractor at
late-times. Our framework therefore unifies early and late dark energy using a
single scalar degree of freedom. We analyze a fiducial attractive early dark
energy model and find that it is disfavored by cosmological data due to the
presence of a long-lived saddle point in the matter era where the scalar plays
the role of an additional component of (non-clustering) dark matter. Our
investigations provide lessons for future model-building efforts aimed at
constructing viable attractive early dark energy models.
