Removing the big bang singularity: the role of the generalized uncertainty principle in quantum gravity

Abstract

The possibility of avoiding the big bang singularity by means of a generalized uncertainty principle is investigated. In relation with this matter, the statistical mechanics of a free-particle system obeying the generalized uncertainty principle is studied and it is shown that the entropy of the system has a finite value in the infinite temperature limit. It is then argued that negative temperatures and negative pressures are possible in this system. Finally, it is shown that this model can remove the big bang singularity.

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

“…This means that the one-particle phase space measure is given by h −3 and therefore each integral on the phase space will be of the form d 3 xd 3 ph −3 ( ). For a system obeying the GUP, the volume of phase space cells can be derived in several ways [19,21,22,23,41]. All of them show that the phase space should be divided into cells of volume h 3 (1 + λ 2 p 2 ) 3 and thus phase space integrals are…”

“…This property is an integral part of a system obeying the generalized uncertainty relation (1) [19].…”

“…Using equations (19) and (20), one can infer that the radius R and the total mass M both tend to infinity at the infinite y c limit. Although, it is not difficult to prove that the solution of (17), i.e.…”

“…The main property of the system, which plays the crucial role to achieve this result, is that both the density function ρ e and the particle density n take finite values as the Fermi momentum y tends to infinity and the details of these functions are not important. It means that the number of accessible states of a particle in a finite volume is finite [19]. Therefore, it seems that the result is independent of the model.…”

“…The main property of this Fermi gas is that the density of particle number and the density of internal energy take finite values as the Fermi energy tends to infinity. It is a consequence of this fact that the number of accessible states of a particle obeying the generalized uncertainty principle (1) in a finite volume is finite [19]. Then we apply the equation of state of such a Fermi gas to the Newtonian hydrostatic equation which is describing the equilibrium configuration of a white dwarf.…”