Late time transitions in the quintessence field and the $H_0$ tension

TL;DR

The paper investigates whether a late-time quintessence transition, where a field tracks matter around recombination and evolves to a late-time equation of state $w_{\phi0}$, can ease the $H_0$ tension observed between local distance-ladder measurements and CMB in $\Lambda$CDM. It introduces a smooth transition parameterised by $a_*$ and $\Delta$, implements a field-theory realisation with metastable minima, and analyzes cosmological data via CAMB/CosmoMC across extended parameter spaces. The main finding is that such late-time transitions do not alleviate the $H_0$ (nor $S_8$) tension; transitions must occur early ($\log_{10}(a_*)\lesssim-1$) and $f_L$ remains unconstrained, with $w_{\phi0}$ anticorrelating with $H_0$ when allowed to vary. The results support the view that solutions to the $H_0$ problem more plausibly involve modifications to early-Universe physics and the sound horizon rather than late-time quintessence dynamics.

Abstract

We consider a quintessence field which transitions from a matter-like to a cosmological constant behavior between recombination and the present time. We aim at easing the tension in the measurement of the present Hubble rate, and we assess the $Λ$CDM model properly enlarged to include our quintessence field against cosmological observations. The model does not address the scope we proposed. This result allows us to exclude a class of quintessential models as a solution to the tension in the Hubble constant measurements.

Figures (13)

• Figure 1: The equation of state $w_{\rm \phi \,eff}(a)$ in Eq. \ref{['eq:weff']} as a function of the scale factor $a$, for different values of the parameters $a_*$ and $\Delta$. See the text for additional details.
• Figure 2: The energy density of the quintessence field $\rho_{\rm \phi \,eff}(a)$ in Eq. \ref{['eq:energydensity']} as a function of the scale factor $a$, for the same values of the parameters $a_*$ and $\Delta$ as in Fig. \ref{['fig:wphi']}. See the text for additional details.
• Figure 3: The potential $V(\phi)$ in units of $(mf)^2$, as a function of the field configuration in units of the energy scale $f$. The coloring labels the different values of the parameter $\kappa = \Lambda^2/mf$ considered.
• Figure 4: Time evolution of the absolute value of $\phi(t)/f$ as a function of $t/t_*$, for different values of $\kappa$. The dashed lines show the values of $\Lambda^2/m$ for each value of $\kappa$ considered. The dotted line is a fit to a matter-like behavior, for which $\phi \propto a^{-3/2}$.
• Figure 5: Evolution of the energy density in the quintessence field (black solid line), radiation (red dotted line), and matter (blue dashed line), as a function of the scale factor $a$. The quintessence field is described by the equation of state in Eq. \ref{['eq:weff']} with $\Delta = 0.5$, $a_* = 10^{-1}$, $f_L= 0$, and $w_{\phi 0} = -1$, see the text for additional detail. For each species $i$, the corresponding energy density $\rho_i$ is measured in units of the present critical density $\rho_{\rm crit} = 3M_{\rm PL}^2H_0^2$.