Abstract
We investigate the quintessence scalar field model modified by the generalized uncertainty principle in the background of a spatially flat homogeneous and isotropic universe. By performing a dynamical system analysis we examine the nature of the critical points and their stability for two potentials, one is the exponential potential and the other is a general potential. In the case of an exponential potential, we find some new critical points for this modified quintessence scenario that describe the de Sitter universes, and these critical points do not appear in the standard quintessence model with an exponential potential. This is one of the main results of this work. Now for the general potential our analysis shows that the physical properties of the critical points remain exactly the same as for the exponential potential which means that within this modified quintessence scenario all kind of potentials have same behaviour. This kind of result is completely new in cosmology because with the change of the potential, differences are usually expected in all respect.
Highlights
The effects of generalized uncertainty principle (GUP) in various cosmological theories can be studied in order to see whether such effects give rise to some interesting directions related the dynamical history of the universe
The quantum gravity theory predicts the existence of a minimum length scale of the order of the Planck length lpl and this motivated to generalize the Heisenberg’s uncertainty principle to some
The generalized uncertainty principle has been found to be very effective to explain several important issues that are directly related to our universe and its evolution
Summary
Concerning the early evolution of the universe, considerable attention on the nature of the gravitational theory at the quantum level has been paid by many investigators. All of them reported the existence of a minimum length scale of the order of the Planck length lpl (equivalently, there exists a maximum energy scale in nature) This motivated to generalize the Heisenberg’s uncertainty principle to some generalized uncertainty principle (GUP) in quantum gravity [27]. Whether the black holes will completely evaporate to either photons, ordinary matter particles or vacuum, or whatever it be (some remnant for instance) is highly questionable due to the lack of a definite quantum gravitational theory (see the discussions [33,34,35,36,37]). When the black hole will reach the Planck size, it will stop radiating and its entropy reaches zero while its effective temperature will reach the maximum limit, and it reduces to an inert remnant having no radiating power, but only gravitational interactions may exist.
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