The $H_0$ and $S_8$ tensions necessitate early and late time changes to
  $\Lambda$CDM
  An only early or only late time alteration to $\Lambda$CDM has been
inadequate at resolving both the $H_0$ and $S_8$ tensions simultaneously;
however, a combination of early and late time alterations to $\Lambda$CDM can
provide a solution to both tensions. As an illustration, we examine a combined
Early Dark Energy - Decaying Dark Matter model. While early dark energy has the
ability to resolve the $H_0$ tension, it leads to a discrepancy in $S_8$
measurements. We show that the addition of decaying dark matter helps resolve
the $S_8$ discrepancy that would otherwise be enhanced in an early dark energy
model, while the latter is able to relieve the $H_0$ disagreement to within the
95th percentile interval. Our results show a preference for the combined model
over $\Lambda$CDM with $\Delta \rm{AIC} = -6.72$, hinting that both early and
late universe modifications may be necessary to address the cosmological
tensions.
