# Implications of a transition in the dark energy equation of state for the $H_0$ and $\sigma_8$ tensions

## TL;DR

This paper investigates a rapid transition in dark energy's equation of state between redshifts 1 and 2, proposing it as a solution to current Hubble constant and structure growth tensions, with measurable implications for upcoming surveys.

## Contribution

It introduces a model of dark energy transition that aligns with low-redshift observations and addresses the $H_0$ and $\sigma_8$ tensions, supported by Gaussian process and parametric analyses.

## Key findings

- Dark energy was negligible around z=2 but is significant today.
- The transition leads to slower growth of perturbations at z<1.
- This model can alleviate the $\sigma_8$ tension with upcoming measurements.

## Abstract

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.