|
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 M4P
.
|