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 $H_0=73\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$ to within 1% and the high-redshift expansion history is unchanged from the $\mathrm{\Lambda }$CDM inference by the Planck satellite. Dark energy was effectively non-existent around $z=2$, but its density is close to the $\mathrm{\Lambda }$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 $\mathrm{\Lambda }$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.