Zeta functions in brane world cosmology

Antonino Flachi, Alan Knapman, Wade Naylor, Misao Sasaki

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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.

Original languageEnglish
Number of pages1
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume70
Issue number12
DOIs
Publication statusPublished - 2004 Jan 1
Externally publishedYes

Fingerprint

determinants
cosmology
balls
conformal mapping
differential operators
curvature
scalars
operators
radii

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

Cite this

Zeta functions in brane world cosmology. / Flachi, Antonino; Knapman, Alan; Naylor, Wade; Sasaki, Misao.

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 70, No. 12, 01.01.2004.

Research output: Contribution to journalArticle

Flachi, Antonino ; Knapman, Alan ; Naylor, Wade ; Sasaki, Misao. / Zeta functions in brane world cosmology. In: Physical Review D - Particles, Fields, Gravitation and Cosmology. 2004 ; Vol. 70, No. 12.
@article{85658cf89f284aa6806b8a703cf3d298,
title = "Zeta functions in brane world cosmology",
abstract = "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.",
author = "Antonino Flachi and Alan Knapman and Wade Naylor and Misao Sasaki",
year = "2004",
month = "1",
day = "1",
doi = "10.1103/PhysRevD.70.124011",
language = "English",
volume = "70",
journal = "Physical review D: Particles and fields",
issn = "1550-7998",
publisher = "American Institute of Physics",
number = "12",

}

TY - JOUR

T1 - Zeta functions in brane world cosmology

AU - Flachi, Antonino

AU - Knapman, Alan

AU - Naylor, Wade

AU - Sasaki, Misao

PY - 2004/1/1

Y1 - 2004/1/1

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=85039603949&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039603949&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.70.124011

DO - 10.1103/PhysRevD.70.124011

M3 - Article

VL - 70

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -