  We present a new class of models that have potential to alleviate tensions
present in the cosmological data today. We postulate variation in the sound
horizon scale on super-horizon scales, i.e. on scales that are larger than that
of the present observable low-redshift universe ($\gtrsim 1\,$Gpc) while at the
same time smaller than the largest scales probed by the cosmic microwave
background (CMB) ($\lesssim10\,$Gpc). In this scenario, CMB peaks are naturally
smoothed as preferred by the Planck data, while at the same time the
low-redshift baryon acoustic oscillation calibration is partially decoupled
from the CMB. Taking super-horizon variations in baryon fraction as an example
and using approximate modeling, we find improvement in the best fit Planck
power spectrum model $\Delta \chi^2 \sim 6$ for one extra degree of freedom
with the relevant extension parameter $10^3 \sigma_b = 2.12 \pm 0.50 $,
implying about 10\% variations in baryon fraction across the universe. At the
same time, $S_8$ drops by about 1 sigma, easing tension with weak lensing
surveys. While $H_0$ increases in this model by about 1 sigma, this is
insufficient to explain the Hubble tension in $\Lambda$CDM. Since the power of
low redshift BAO is relaxed, we find that the combination of Planck 2018 data,
eBOSS BAO data and Riess et al distance ladder Hubble parameter determination
produce a satisfactory fit in the model with free dark energy equation of
state. Such a fit, however, favors a phantom dark energy equation of state
$w<-1$ at 2-3 sigma.
