IJPAM: Volume 49, No. 4 (2008)


Peter K.F. Kuhfittig
Department of Mathematics
Milwaukee School of Engineering
1025, N. Broadway, Milwaukee, WI 53202, USA
e-mail: kuhfitti@msoe.edu

Abstract.In the usual brane-world scenario matter fields are confined to the four-dimensional spacetime, called a 3-brane, embedded in a higher-dimensional space, usually referred to as the bulk spacetime. In this paper we assume that the 3-brane is a de Sitter space; there is only one extra spatial dimension, assumed to be time dependent. By using the form of the brane-world energy-momentum tensor suggested by Shiromizu et al in the five-dimensional Einstein equations, it is proposed that the cosmological expansion of the 3-brane may provide a possible explanation for the collapse of the extra dimension. More precisely, whenever the bulk cosmological constant $\Lambda$ is negative, the extra spatial dimension rapidly shrinks during the inflation of the brane. When $\Lambda$ is positive, on the other hand, the extra spatial dimension either completely follows the cosmological expansion of the brane or completely ignores it, thereby shrinking relative to the expanding space. This behavior resembles the all-or-nothing behavior of ordinary systems in an expanding universe, as recently demonstrated by R.H. Price.

Received: August 14, 2008

AMS Subject Classification: 83C05

Key Words and Phrases: brane world, extra spatial dimension

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4