Beyond $\Lambda$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 $\Lambda$(t) within the spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) framework. Here we study a power-law $\Lambda(t)$CDM model characterized by a dynamic cosmological constant expressed as a function of the Hubble parameter and its derivative $\Lambda(t)$ $=\alpha (\dot H+H^{2})+\lambda H^2+4\pi G\rho\eta.$ 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 $\sim1.5\sigma$. 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 $\Lambda(t)$ model provides a viable alternative to the standard $\Lambda$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 $\Lambda$CDM . The model also demonstrates compatibility with late-time Hubble parameter observations and offers a compelling framework to address the limitations of $\Lambda$CDM.