Authors

Citation

R. Mansouri et F. Nasseri, Model universe with variable space dimension: Its dynamics and wave function - art. no. 123512, PHYS REV D, 6012(12), 1999, pp. 3512

Citations number

70

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Physics

Journal title

PHYSICAL REVIEW D

ISSN journal

0556-2821
→ ACNP

Volume

6012

Issue

12

Year of publication

1999

Database

ISI

SICI code

0556-2821(199912)6012:12<3512:MUWVSD>2.0.ZU;2-O

Abstract

Assuming the space dimension is not constant, but varies with the expansion
of the universe, a Lagrangian formulation of a toy universe model is given
. After a critical review of previous works, the field equations are derive
d and discussed. It is shown that this generalization of the FRW cosmology
is not unique. There is a free parameter in the theory, C, with which we ca
n fix the dimension of space, say, at the Planck time. Different possibilit
ies for this dimension are discussed. The standard FRW model corresponds to
the limiting case C --> + infinity+. Depending on the free parameter of th
e theory, C, the expansion of the model can behave differently from the sta
ndard cosmological models with constant dimension. This is explicitly studi
ed in the framework of quantum cosmology. The Wheeler-DeWitt equation is wr
itten down. It turns out that in our model universe, the potential of the W
heeler-DeWitt equation has different characteristics relative to the potent
ial of the de Sitter minisuperspace. Using the appropriate boundary conditi
ons and the semiclassical approximation, we calculate the wave function of
our model universe. In the limit of C --> + infinity, corresponding to the
case of constant space dimension, our wave function does not have a unique
behavior. It can either lead to the Hartle-Hawking wave function or to a mo
dified Linde wave function, or to a more general one, but not to that of Vi
lenkin. We also calculate the probability density in our model universe. It
is always more than the probability density of the de Sitter minisuperspac
e in three-space as suggested by Vilenkin, Linde, and others. In the limit
of constant space dimension, the probability density of our model universe
approaches that of the Vilenkin and Linde probability density, being exp(-2
\S-E\), where SE is the Euclidean action. Our model universe indicates ther
efore that the Vilenkin wave function is not stable with respect to the var
iation of space dimension. [S0556-2821(99)03322-6].