Cosmological model from the holographic equipartition law with a modified R\'{e}nyi entropy

Understand

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 R\'{e}nyi 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 R\'{e}nyi 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.