Implications of a transition in the dark energy equation of state for the $H_0$ and $σ_8$ tensions

TL;DR

The paper investigates whether a rapid transition in the dark energy density between redshifts 1 and 2 can alleviate the H0 and σ8 tensions while preserving Planck-era expansion. It employs a model-independent Gaussian process reconstruction of the expansion history with a forecasted 1% H0 precision, and a concrete Transitional Dark Energy (TDE) parameterization, showing a preference for a late-time DE transition that yields slower growth and fewer SZ clusters. The TDE scenario fits current data with strong Bayesian evidence over ΛCDM under their assumptions and makes testable predictions for growth observables and cluster counts in upcoming surveys. Internal consistency tests indicate tensions remain in BAO/SN calibrations, but the overall framework provides a concrete, falsifiable path to reconciling late-time cosmology with high-precision CMB constraints.

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 $Λ$CDM inference by the Planck satellite. Dark energy was effectively non-existent around $z=2$, but its density is close to the $Λ$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 $Λ$CDM, that is measurable by upcoming surveys and can alleviate the $σ_8$ tension between the Planck CMB temperature and low-redshift probes of the large-scale structure.

Figures (16)

• Figure 1: Posteriors for the expansion history as determined by the GP regression (inner 68% and outer 95% confidence levels). The Hubble and angular diameter distances, $D_H(z)$ and $D_A(z)$, are shown in the top and bottom panels, respectively. These distances are shown relative to the fiducial Planck $\Lambda$CDM model. The orange shaded regions correspond to the results with the Riess et al. (2016) Riess:2016jrr uncertainty on $H_0$ as calculated in J18, while the blue shaded regions correspond to forecasts with 1% precision on $H_0$. The orange and blue solid lines illustrate the median results of the GPs. Note the split linear-logarithmic redshift axis.
• Figure 2: The top panel of the figure shows the inferred dark energy equation of state as a function of redshift from the GP regression. The bottom panel shows the growth rate $f = d\ln(D)/d\ln(a)$ from the GP regression. As in Fig. \ref{['fig:main']}, the blue shaded regions correspond to the 68% and 95% confidence levels and the solid line corresponds to the median of the GP inference. The black solid line in the bottom panel corresponds to the $\Lambda$CDM growth rate.
• Figure 3: Posteriors of $H_0$ and representative derived parameters from the MCMC inference of the TDE model (inner 68% CL, outer 95% CL), fitting the same datasets as the GP. Each of these panels show the derived parameter evaluated at $z=0$, $z=0.5$, and $z=2$ (blue, green, violet). These representative parameters are the equation of state (left), dark energy density scaled to the present critical density (center left), $f\sigma_8$ (center right), and $\sigma_8$ (right). The dashed horizontal lines correspond to the fiducial $\Lambda$CDM values for $w(z)$$f \sigma_8 (z)$ and $\sigma_8 (z)$.
• Figure 4: Sunyaev-Zel'dovich cluster counts $dN/dM/dz$ for a $\Lambda$CDM model consistent with Planck (black), a $\Lambda$CDM model with $\sigma_8=0.75$ (green), and an example TDE model (red). The shaded bands correspond to the cosmic variance 68% and 95% CLs.
• Figure 5: Posteriors of $H_0$ and $w(z)$ for $z=0,0.5,2.0$ (blue, green violet) for the cases where $r_{\rm drag}$ is varied independently (left) and scaled linearly with $D_H(z_*)$ (right). The black dashed line corresponds to the $\Lambda$CDM equation of state $w=-1$.