Barrow entropic cosmology with exponential potential field

In this paper, we consider an exponential potential [Formula: see text] in the framework of Barrow entropy under the constant-roll inflation and check their viability in the light of observable Planck 2020 data. By applying the first law of thermodynamics to the apparent horizon of the Universe, a modification of the Friedmann–Robertson–Walker (FRW) metric is derived in the context of Barrow entropy. We consider the early inflationary period of the universe to consist phenomenologically of a single inflationary state, that is, a state of the costant-roll inflation in which inflation is driven by an exponential potential field function. By fitting the constant-roll inflationary models to the observations, we examined the effect of the Barrow parameter [Formula: see text] on the inflation mechanism with the constant-roll parameter [Formula: see text]. As a result, we concluded that for a viable inflation, the observation limits of the inflation parameters determine that the constant-roll parameter is in the range [Formula: see text].