Entropic cosmology with the Rényi entropy of the apparent horizon SR=(1/α)ln(1+αSBH), where SBH is the Bekenstein–Hawking entropy, is studied. By virtue of the thermodynamics–gravity correspondence, a model of dark energy is investigated. The generalized Friedmann equations for the Friedmann–Lemaître–Robertson–Walker spatially flat universe with barotropic matter fluid are obtained. We compute the dark energy density ρD, pressure pD, and the deceleration parameter q of the universe. At some model parameters, the normalized density parameter of the matter Ωm0≈0.315 and the deceleration parameter q0≈−0.535 for the current epoch, which are in the agreement with the Planck data, are found. Making use of the thermodynamics–gravity correspondence, we describe the late-time acceleration of the universe. The entropic cosmology considered here is equivalent to cosmology based on the teleparallel gravity with the definite function F(T). The Hubble parameters are in approximate agreement (within 5 percents) with the observational Hubble data for redshifts 0.07≤z≤1.75 at the entropy parameter α≈0.305GH02.
S. I. Kruglov (Mon,) studied this question.