Cosmological constraints on time-varying cosmological terms: A study of FLRW universe models with $\Lambda(t)$CDM cosmology

This paper explores models of the FLRW universe that incorporate a time-varying cosmological term $\Lambda(t)$. Specifically, we assume a power-law form for the cosmological term as a function of the scale factor: $\Lambda(t)=\Lambda_{0} a(t)^{-\alpha}$, where $\Lambda_{0}$ represents the present value of the cosmological term. Then, we derive an exact solution to Einstein's field equations within the framework of $\Lambda(t)$CDM cosmology and determine the best-fit values of the model parameters using the combined $H(z)$ + SNe Ia dataset and MCMC analysis. Moreover, the deceleration parameter demonstrates the accelerating behavior of the universe, highlighting the transition redshift $z_{tr}$, at which the expansion shifts from deceleration to acceleration, with confidence levels of $1-\sigma$ and $2-\sigma$. In addition, we analyze the behavior of the Hubble parameter, jerk parameter, and $Om(z)$ diagnostic. Our analysis leads us to the conclusion that the $\Lambda(t)$CDM model is consistent with present-day observations.