Einstein static universe, GUP, and natural IR and UV cut-offs

Abstract

We study the Einstein static universe (ESU) in the framework of Generalized Uncertainty Principle (GUP) constructed by the Snyder non-commutative space. It is shown that the deformation parameter can induce an effective energy density subject to GUP which obeys the holographic principle (HP) and plays the role of a cosmological constant. Using the holographic feature of this effective energy density, we introduce natural IR and UV cut-offs which depend on the GUP-based effective equation of state. Moreover, we propose a solution to the cosmological constant problem (CCP). This solution is based on the result that the Einstein equations just couple to the tiny holographic-based surface energy density (cosmological constant) induced by the deformation parameter, rather than the large quantum gravitational-based volume energy density (vacuum energy) having contributions of order [Formula: see text].