Determining scalar field potential in power-law cosmology with observational data

In power-law cosmology, we determine potential function of a canonical scalar field in FLRW universe in presence of barotropic perfect fluid. The combined WMAP5+BAO+SN dataset and WMAP5 dataset are used here to determine the value of the potential. The datasets suggest slightly closed universe. If the universe is closed, the exponents of the power-law cosmology are $q = 1.01$ (WMAP5 dataset) and $q=0.985$ (combined dataset). The lower limits of $a_0$ (closed geometry) are $5.1\E{26}$ for WMAP5 dataset and $9.85\E{26}$ for the combined dataset. The domination of the power-law term over the curvature and barotropic density terms is characterised by the inflection of the potential curve. This happens when the universe is 5.3 Gyr old for both datasets.