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

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. 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.Comment: Final version accepted for publication in EPJC. The titile is revised and references are added. [12 pages, 4 figures

Belyi Function whose Grothendieck Dessin is a Flower Tree with Two Ramification Indices

In this paper we present an explicit construction of Belyi functions whose dessins are flower trees (i.e., graphs of diameter 4) with two ramification indices. We also give a method for obtaining Belyi functions defined over the moduli fields of the dessins.</p