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 H _ { 0 } value 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 .