Evaluating a Sigmoid Dark Energy Model to Explain the Hubble Tension

Abstract

In this study we analyze Type Ia supernovae (SNe Ia) data sourced from the Pantheon+ compilation \citep{pantheon} to investigate late-time physics effects influencing theexpansion history, \(H(z)\) , at redshifts \((z < 2)\) . Our focus centers on a time-varying dark energy (DE) model that introduces a rapid transition in the equation of state, at a specific redshift, \(z_a\) , from the baseline, \(\Lambda = -1\) , value to the present value, \(w_0\) , through the implementation of a sigmoid function.The constraints obtained for the DE sigmoid phenomenological parametrization have broad applicability for dynamic DE models that invoke late-time physics.Our analysis indicates that the sigmoid model provides a slightly better, though not statistically significant, fit to the SNe Pantheon+ data compared to the standard \lcdm\alone. The fit results, assuminga flat geometry and maintaining \(\Omega_m\) constant at the 2018-Planck value of $0.3153$, are as follows: \(H_0 = 73.3^{+0.2}_{-0.6} \) \ksmpc\, \(w_{0} = -0.95^{+0.15}_{-0.02} \), \(z_a = 0.8 \pm 0.46\). The errors represent statistical uncertainties only.The available SN dataset lacks sufficient statistical power to distinguish between the baseline \lcdm\and the alternative sigmoid models.A feature of interest offered by the sigmoid model is that it identifies a specific redshift, $z_a = 0.8$, where a potential transitionin the equation of state could have occurred. The sigmoid model does not favor a DE in the phantom region ($w_0 < -1$). Further constraints to the dynamic DE model have been obtained using CMB data to compute the distance to the last scattering surface. While the sigmoid DE modeldoes not completely resolve the $H_0$ tension, it offers a transition mechanismthat can still play a role alongside other potential solutions.