Implications of a transition in the dark energy equation of state for
  the $H_0$ and $\sigma_8$ tensions
  We explore the implications of a rapid appearance of dark energy between the
redshifts ($z$) of one and two on the expansion rate and growth of
perturbations. Using both Gaussian process regression and a parameteric model,
we show that this is the preferred solution to the current set of low-redshift
($z<3$) distance measurements if $H_0=73~\rm km\,s^{-1}\,Mpc^{-1}$ to within
1\% and the high-redshift expansion history is unchanged from the $\Lambda$CDM
inference by the Planck satellite. Dark energy was effectively non-existent
around $z=2$, but its density is close to the $\Lambda$CDM model value today,
with an equation of state greater than $-1$ at $z<0.5$. If sources of
clustering other than matter are negligible, we show that this expansion
history leads to slower growth of perturbations at $z<1$, compared to
$\Lambda$CDM, that is measurable by upcoming surveys and can alleviate the
$\sigma_8$ tension between the Planck CMB temperature and low-redshift probes
of the large-scale structure.
