It has recently been shown that the thermodynamics of a FRW universe can be fully derived using the generalized uncertainty principle (GUP) in extra dimensions as a primary input. There is a phenomenologically close relation between the GUP and Modified Dispersion Relations (MDR). However, the form of the MDR in theories with extra dimensions is as yet not known. The purpose of this letter is to derive the MDR in extra dimensional scenarios. To achieve this goal, we focus our attention on the thermodynamics of a FRW universe within a proposed MDR in an extra dimensional model universe. We then compare our results with the well-known results for the thermodynamics of a FRW universe in an extra dimensional GUP setup. The result shows that the entropy functionals calculated in these two approaches are the same, pointing to a possible conclusion that these approaches are equivalent. In this way, we derive the MDR form in a model universe with extra dimensions that would have interesting implications on the construction of the ultimate quantum gravity scenario.Comment: 9 pages, to appear in PL

The entropy of the Reissner-N\"{o}rdstrom black hole is studied within the context of a brane-world scenario. Such a black hole is a solution of the Einstein field equations on the brane, possessing a tidal charge which is a reflection of the extra dimension. We use the modified dispersion relation to obtain the entropy of such brane-world black holes. The resulting entropy differs from that of the standard Bekenstein-Hawking's and contains information on the extra dimension.Comment: 9 pages, 4 figures, to appear in PL

We use the collision-free Boltzmann equation in Palatini f (R) gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contribute to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in cluster of galaxies. We then derive the velocity dispersion relation for clusters followed by the metric tensor components inside the cluster as well as the f (R) lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the f (R) virial theorem is a convenient tool to test the viability of f (R) theories in different models. Finally, we discuss the limitations of our approach in the light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work. 04.20.Cv PACS

In Verlinde's formalism, gravity is an emergent phenomenon which can be interpreted as an entropic force. Borrowing the modified entropy-area relation from rainbow gravity, one can derive the corrections to the gravitational force from the viewpoint of entropic force. The modified gravitational force can be used to find the Friedmann equation in the Friedmann-Robertson-Walker (FRW) universe in the realm of high-energy physics.

The modified dispersion relation as a common feature of all quantum gravity scenarios provides a perturbation framework upon which the black hole thermodynamics can be corrected. In this letter, we obtain the corrections to the d-dimensional Schwarzschild black hole thermodynamics by utilizing the extra dimensional form of the modified dispersion relation, leading to the modification of the Cardy-Verlinde formula. Furthermore, we show that the modified dispersion relation corrections to the Cardy-Verlinde formula can be taken into account by redefining the Virasoro operator and the central charge. *