Beyond $\mathrm{\Lambda }$CDM: Exploring a Dynamical Cosmological Constant Framework Consistent with Late-Time Observations

In this work, we investigate a cosmological scenario with a time-dependent cosmological constant $\mathrm{\Lambda }$(t) within the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) framework. Here we study a power-law $\mathrm{\Lambda }(t)$CDM model characterized by a dynamic cosmological constant expressed as a function of the Hubble parameter and its derivative $\mathrm{\Lambda }(t)$ $=\alpha (\dot{H}+H^2)+\lambda H^2+4\pi G\rho \eta \mathrm{.}$ Using recent observational datasets (DESI BAO, OHD, and PP&SH0ES), we constrain the model’s free parameters $(H_0,\alpha ,\lambda ,\eta )$ 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 $\sim 1.5\sigma$. The reconstructed $Om$ diagnostic exhibits a negative slope, indicating a dynamic dark energy behavior with quintessence-like characteristics ($\omega >-1$). These results suggest that the proposed $\mathrm{\Lambda }(t)$ model provides a viable alternative to the standard $\mathrm{\Lambda }$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 $\mathrm{\Lambda }$CDM . The model also demonstrates compatibility with late-time Hubble parameter observations and offers a compelling framework to address the limitations of $\mathrm{\Lambda }$CDM.