TY - JOUR

T1 - Zeta functions in brane world cosmology

AU - Flachi, Antonino

AU - Knapman, Alan

AU - Naylor, Wade

AU - Sasaki, Misao

N1 - Funding Information:
. We also thank I. Moss, J. Norman, and W. Santiago-Germán for help in sorting out the transcription errors in Ref. . A. F. is indebted to L. Da Rold, R. Fiore, J. Garriga, and A. Papa for discussions at the early stage of this work and acknowledges the kind hospitality of the Department of Physics of the Università della Calabria, where part of this work was carried out. A. F. is supported by the JSPS under Contract No. P04724. W. N. is supported by the program, Grant-in-Aid for the 21st Century COE, “Center for Diversity and Universality in Physics,” at Kyoto University. M. S. is supported in part by Monbukagakusho Grant-in-Aid for Scientific Research(S) No. 14102004. We would like to thank Y. Himemoto, S. Nojiri, S. Ogushi, O. Pujolàs, T. Tanaka, and D. Toms for useful comments. We thank I. Moss for pointing out the ill-defined nature of the conformal transformation used in Refs.

PY - 2004/12

Y1 - 2004/12

N2 - 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 back ground, 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.

AB - 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 back ground, 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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U2 - 10.1103/PhysRevD.70.124011

DO - 10.1103/PhysRevD.70.124011

M3 - Article

AN - SCOPUS:19944419649

SN - 0556-2821

VL - 70

SP - 124011-1-124011-13

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 12

M1 - 124011

ER -