Abstract:
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.
