Towards a Cosmology with Minimal Length and Maximal Energy

Abstract

The Friedmann-Robertson-Walker (FRW) universe and Bianchi I,II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts minimum measurable length as well as maximum measurable momentum. We get a dynamic cosmological bounce for the FRW universe. With Bianchi universe, we found that the universe may be still isotropic by implementing GUP. Moreover, the wall velocity appears to be stationary with respect to the universe velocity which means that when the momentum of the Universe evolves into a maximum measurable energy, the bounce is enhanced against the wall which means no maximum limit angle is manifested anymore.