An accelerating flat FLRW model with observation constraints and dynamic Λ

In this paper, we explore power law solution of FLRW universe model that is associated with a variable cosmological term [Formula: see text] as a linear function of [Formula: see text] and [Formula: see text]. The model parameters were estimated on the basis of the four datasets: The Hubble 46 data and the Union 2.1 compilation datasets comprise distance modulus of 580 SNIa supernovae at different redshifts, the Pantheon dataset which contains Apparent magnitudes of 1048 SNIa supernovae at various redshifts and finally BAO dataset of volume averaged distances at 5 redshifts. We employ the conventional Bayesian methodology to analyze the observational data and also the Markov Chain Monte Carlo (MCMC) technique to derive the posterior distributions of the parameters. The best-fit values of Hubble parameter [Formula: see text] as per the four datasets are found as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], respectively. Of late the present value of Hubble parameters [Formula: see text] was empirically given as 73 and 67.7[Formula: see text](km/s)/Mpc using distance ladder techniques and measurements of the cosmic microwave background. The OHD+BAO+Union and OHD+Pan+BAO+Union combined datasets provide the best-fit Hubble parameter value [Formula: see text] as [Formula: see text] and [Formula: see text], respectively. The various geometrical and physical properties of the model were also investigated and were found in good agreement with observations.