Beyond $Λ$CDM: Exploring a Dynamical Cosmological Constant Framework Consistent with Late-Time Observations

TL;DR

This work investigates a dynamical vacuum energy model in a flat FLRW universe by parameterizing the cosmological constant as $\Lambda(t)=\alpha(\dot H+H^2)+\lambda H^2+4\pi G\rho\eta$. Using DESI BAO, OHD, and PP&SH0ES data with MCMC inference, it constrains $(H_0,\alpha,\lambda,\eta)$ and finds $H_0\approx71.9$ km s$^{-1}$ Mpc$^{-1}$, significantly reducing the Hubble tension to about $1.3$–$1.5\sigma$ relative to SH0ES, while Planck tension remains. The reconstructed $Om(z)$ is negative, signaling quintessence-like dark energy ($\omega>-1$), and $\Omega_{\Lambda0}$ ranges from about $0.48$ to $0.62$ depending on dataset, with $\omega_{\rm tot}\approx-0.32$ to $-0.66$. The model provides a competitive, physically motivated alternative to $\Lambda$CDM for late-time acceleration and motivates further observational tests with upcoming data. $\Lambda(t)$CDM thus offers a framework to address the limitations of $\Lambda$CDM while remaining compatible with current late-time observations.

Abstract

In this work, we investigate a cosmological scenario with a time-dependent cosmological constant $Λ$(t) within the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) framework. Here we study a power-law $Λ(t)$CDM model characterized by a dynamic cosmological constant expressed as a function of the Hubble parameter and its derivative $Λ(t)$ $=α(\dot H+H^{2})+λH^2+4πGρη.$ Using recent observational datasets (DESI BAO, OHD, and PP\&SH0ES), we constrain the model's free parameters $(H_{0},α,λ,η)$ and analyze their impact on key cosmological quantities. A Markov chain Monte Carlo (MCMC) analysis of the best-fit value of $H_{0}=71.9\pm 0.23$ km/s/Mpc from PP\&SH0ES analysis only, which substantially alleviates the existing tension between early and late-time determinations of the Hubble constant, reducing it to $\sim1.5σ$. The reconstructed $Om$ diagnostic exhibits a negative slope, indicating a dynamic dark energy behavior with quintessence-like characteristics ($ω>-1$). These results suggest that the proposed $Λ(t)$ model provides a viable alternative to the standard $Λ$CDM paradigm to explain the late-time acceleration of the universe. Our findings show that this model alleviates the Hubble tension more effectively than the standard $Λ$CDM . The model also demonstrates compatibility with late-time Hubble parameter observations and offers a compelling framework to address the limitations of $Λ$CDM.

Figures (5)

• Figure 1: The free parameters constraints of the $\Lambda(t)$CDM model are presented at the 1$\sigma$ and 2$\sigma$ confidence levels, based on the combined analysis of DESI BAO, OHD, and PP&SH0ES data.
• Figure 2: The 2D plot shows how the Power Law model diverges/converges from the $\Lambda$CDM model, in comparison with 33 observation Hubble parameter data points with corresponding error bars.
• Figure 3: The 2D plot shows the distance modulus $\mu(z)$ for the Power law model (red line) and the $\Lambda$CDM model (black dotted line), alongside 1701 Pantheon Plus and SH0ES data points with corresponding blue colour error bars.
• Figure 4: The left panel displays Om(z) diagnostic with respect to $z$ and the right panel shows $\Lambda$(z) with respect to $z$ with Power law model from all the considered datasets.
• Figure 5: The 1D plot $H_0(t_0 - t)$ vs z with Power law model from OHD, PP&SH0ES, and DESI+OHD+PP&SH0ES datasets