Thermodynamically consistent entropic-force cosmology

We analyze the thermodynamical consistency of entropic-force cosmological models. Our analysis is based on a generalized entropy scaling with an arbitrary power Hubble radius. The Bekenstein-Hawking entropy, proportional to area, and nonadditive $S_{\delta=3/2}$-entropy, volume, are particular cases. One points be solved by cosmology for being taken as serious alternative mainstream provide physical principle that out what temperature have used. determine universe horizon requiring Legendre structure thermodynamics preserved. compare performance thermodynamically consistent models regard available supernovae data providing appropriate constraints optimizing entropies temperatures screen. results point differs from Hawking one.