Constraints on 5D anti-de Sitter embeddings

Physical Review D

Volumn 64, Issue 6, 2001, Pages

  Mannheim, Philip D ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; GEOMETRY; GRAVITY; MATHEMATICAL ANALYSIS; PHYSICS;

EID: 0035884316     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.64.065008     Document Type: Article

References (26)

1. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).
2. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).
3. μν in the static Minkowski embedded brane case given in Eq. (2).
4. S. B. Giddings, E. Katz, and L. Randall, J. High Energy Phys. 03, 023 (2000).
5. 2f], with the coordinate independent gravitational scattering S matrix then being highly suppressed when it involves a scattering between a particle that is localized to the brane and one that is not.
6. While we concentrate here on localization and embedding issues, the Robertson-Walker brane theory has also been studied as a cosmology in and of itself by e.g., C. Csaki, M. Graesser, C. Kolda, and J. Terning, Phys. Lett. B 462, 34 (1999);
7. J. M. Cline, C. Grojean, and G. Servant, Phys. Rev. Lett. 83, 4245 (1999);
8. P. Binetruy, C. Deffayet, and D. Langlois, Nucl. Phys. B565, 269 (2000);
9. P. Binetruy, C. Deffayet, U. Ellwanger, and D. Langlois, Phys. Lett. B 477, 285 (2000);
10. R. N. Mohapatra, A. Perez-Lorenzana, and C. A. de S. Pires, Int. J. Mod. Phys. A 16, 1431 (2001).
11. 5) in such cases, appear not to have been considered in the previous literature.
12. 5 despite the fact that the only matter field in the bulk itself is a bulk cosmological constant.
13. W. Israel, Nuovo Cimento Soc. Ital. Fis., B 44, 1 (1966);
14. W. Israel, Nuovo Cimento Soc. Ital. Fis., B 48, 463(E) (1967).
15. 3=f′/2f in the RW brane case.
16. P. D. Mannheim, Phys. Rev. D 63, 024018 (2001).
17. 2) is kinematically conformai to flat for any f(w)], with the Einstein equations then not only obliging the bulk geometry to be AdS5 but also forcing one of the two α and β coefficients to vanish, to thereby entail only one exponential term.
18. m)/2=-ρ/3, i.e., just like negative pressure quintessence.
19. 5 space is to be the same infinite extent, noncompactified one considered by Randall and Sundrum in the Minkowski brane case.
20. b)=12k.
21. σ;τ acquire (0,5) and (5,5) components in the transformed coordinate system, to thus enable the Israel junction conditions at the brane to be compatible with matter field sources more general than the pure brane cosmological constant source associated with a brane at rest in a warp factor coordinate system. In fact, if the brane were at rest in the Eq. (2) coordinate system, the junction conditions would then require the brane matter fluid to be a pure cosmological constant term. Consequently, once the brane matter fluid departs from a pure cosmological constant, the brane cannot be at rest in the warp factor coordinate system, with the brane extrinsic curvature having to then have an expressly time-dependent discontinuity.
22. 2.
23. 2(t) could still admit of an effective brane-localized current era gravity, with such localization then having only set in during an early universe inflationary phase.
24. ww will only depart from one in fluctuations of the geometry which are less than maximally 3-symmetric.
25. ′2 it in fact does not.
26. 2/2 in the bulk] is then satisfied identically by the solution of Eq. (25).