  Discrepant measurements of the Universe's expansion rate ($H_0$) may signal
physics beyond the standard cosmological model. Here I describe two early
modified gravity mechanisms that reconcile the value of $H_0$ by increasing the
expansion rate in the era of matter-radiation equality. These mechanisms, based
on viable Horndeski theories, require significantly less fine-tuned initial
conditions than early dark energy with oscillating scalar fields. In Imperfect
Dark Energy at Equality (IDEE), the initial energy density dilutes slower than
radiation but faster than matter, naturally peaking around the era of equality.
The minimal IDEE model, a cubic Galileon, is too constrained by the cosmic
microwave background (Planck) and baryon acoustic oscillations (BAO) to relieve
the $H_0$ tension. In Enhanced Early Gravity (EEG), the scalar field value
modulates the cosmological strength of gravity. The minimal EEG model, an
exponentially coupled cubic Galileon, gives a Planck+BAO value $H_0=68.7 \pm
1.5$ (68\% c.l.), reducing the tension with SH0ES from $4.4\sigma$ to
$2.6\sigma$. Additionally, Galileon contributions to cosmic acceleration may
reconcile $H_0$ via Late-Universe Phantom Expansion (LUPE). Combining LUPE, EEG
and $\Lambda$ reduces the tension between Planck, BAO and SH0ES to $2.5\sigma$.
I will also describe additional tests of coupled Galileons based on local
gravity tests, primordial element abundances and gravitational waves. While
further model building is required to fully resolve the $H_0$ problem and
satisfy all available observations, these examples show the wealth of
possibilities to solve cosmological tensions beyond Einstein's General
Relativity.
