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Cosmological equations were recently derived by Padmanabhan from the expansion of cosmic space due to the difference between the degrees of freedom on the surface and in the bulk in a region of space. In this study, a modified Rnyi entropy is applied to Padmanabhan's 'holographic equipartition law', by regarding the Bekenstein-Hawking entropy as a nonextensive Tsallis entropy and using a logarithmic formula of the original Rnyi entropy. Consequently, the acceleration equation including an extra driving term (such as a time-varying cosmological term) can be derived in a homogeneous, isotropic, and spatially flat universe. When a specific condition is mathematically satisfied, the extra driving term is found to be constant-like as if it is a cosmological constant. Interestingly, the order of the constant-like term is naturally consistent with the order of the cosmological constant measured by observations, because the specific condition constrains the value of the constant-like term.
Nobuyoshi KOMATSU (Sat,) studied this question.