On the two new types of the higher order GUP with minimal length uncertainty and maximal momentum

Abstract

In this letter, we present two new types of D-dimensional nonperturbative Generalized Uncertainty Principle (GUP) which are predicted both a minimal length uncertainty and a maximal observable momentum. Then, using these GUPs, we study the density of states for D-dimensional spherical coordinate systems in the momentum space. Also, we investigate the cosmological constant in the presence of these GUPs and finally, compare their massless type with the ones were predicted by Kempf and Pedram in Refs. [1] and [18]. Moreover, using a more general form of the higher order GUP, once again we compare the massless cosmological constants.

Keywords

• Quantum gravity
• Generalized uncertainty principle
• Minimal length uncertainty
• Maximal momentum
• Cosmological constant