Karabat, M. Faruk2025-09-152025-09-1520241793-66320217-7323https://doi.org/10.1142/S0217732324501098https://hdl.handle.net/20.500.12514/9300In this paper, we consider an exponential potential V(φ)=V0e-αφ 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 Δ on the inflation mechanism with the constant-roll parameter γ. 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 0.011≤γ≤0.016. © 2024 Elsevier B.V., All rights reserved.en10.1142/S0217732324501098info:eu-repo/semantics/closedAccessBarrow EntropyConstant-Roll InflationExponential PotentialArticle2-s2.0-85202901458