IJPAM: Volume 49, No. 4 (2008)
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 is negative, the extra spatial dimension
rapidly shrinks during the inflation of the brane. When
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