Zeta Functions in Brane World Cosmology

Details Zeta Functions in Brane World Cosmology Zeta Functions in Brane World Cosmology

2004-10-08

arxiv.org/abs/hep-th/0410083v1

Phys.Rev.D70:124011,2004

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 1 figure

Scientific paper

10.1103/PhysRevD.70.124011

We present a calculation of the zeta function and of the functional determinant for a Laplace-type differential operator, corresponding to a scalar field in a higher dimensional de Sitter brane background, which consists of a higher dimensional anti-de Sitter bulk spacetime bounded by a de Sitter section, representing a brane. Contrary to the existing examples, which all make use of conformal transformations, we evaluate the zeta function working directly with the higher dimensional wave operator. We also consider a generic mass term and coupling to curvature, generalizing previous results. The massless, conformally coupled case is obtained as a limit of the general result and compared with known calculations. In the limit of large anti-de Sitter radius, the zeta determinant for the ball is recovered in perfect agreement with known expressions, providing an interesting check of our result and an alternative way of obtaining the ball determinant.

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