Multi-dimensional cosmology and GUP

Abstract

We consider a multidimensional cosmological model with FRW type metric having 4-dimensional space-time and d-dimensional Ricci-flat internal space sectors with a higher dimensional cosmological constant. We study the classical cosmology in commutative and GUP cases and obtain the corresponding exact solutions for negative and positive cosmological constants. It is shown that for negative cosmological constant, the commutative and GUP cases result in finite size universes with smaller size and longer ages, and larger size and shorter age, respectively. For positive cosmological constant, the commutative and GUP cases result in infinite size universes having late time accelerating behavior in good agreement with current observations. The accelerating phase starts in the GUP case sooner than the commutative case. In both commutative and GUP cases, and for both negative and positive cosmological constants, the internal space is stabilized to the sub-Planck size, at least within the present age of the universe. Then, we study the quantum cosmology by deriving the Wheeler-DeWitt equation, and obtain the exact solutions in the commutative case and the perturbative solutions in GUP case, to first order in the GUP small parameter, for both negative and positive cosmological constants. It is shown that good correspondence exists between the classical and quantum solutions.

Quantum cosmology with dynamical vacuum in a minimal-length scenario

“…We should note that different changes in the WDW equation due to different GUP's have been found in the literature. For example, a linear GUP [38] has led to the emergence of third and fourth order derivatives in the modified WDW equation [2,11,12,39], whereas the KMM GUP [37] has only induced to fourth order derivatives [5,19,47,78]. Those results are in agreement with our modified WDW equation which also displays a term of fourth order derivative in O(β).…”

Interacting dark side of universe through generalized uncertainty principle

“…In addition, the authors of Ref. [40] are studied the effects of the deformed Poisson algebra Eq. (12) in multidimensional cosmology.…”

Multi-Dimensional Cosmology and Dsr–gup

“…and a 0 is the present time compactification scale of the internal space. We introduce the following change of variables provided v 3+d = 1 [13]…”

“…Numerical solution of equations (34) shows that the deformed scale factors like commutative and GUP cases have periodic behavior. To compare with the results obtained in GUP [13], we have included the behaviour of the scale factors in GUP as well as commutative cases within the figures. As is seen in Fig.1, the time interval between big bang and big crunch in GUP case is shortened with respect to commutative one while in DSR-GUP case the time interval between big bang and big crunch is longer.…”