On the cosmological constant problem and brane-world geometry

• Autorzy: Abraão Capistrano , Pedro Odon
• Języki publikacji: EN

Abstrakty

EN

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.

Słowa kluczowe

EN

the cosmological constant problem; brane-world gravity; Nash’s embedding theorem

• Czasopismo: Open Physics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 189-197

Daty

wydano

2011-02-01

online

2010-09-24

Twórcy

autor

Abraão Capistrano

• Universidade Federal do Tocantins, Porto Nacional, TO, 77500-000, Brazil,

autor

Pedro Odon

• Harvard University, Cambridge, MA, USA,

Bibliografia

• [1] W. Nernst, Verh. Dtsch. Phys. Ges. 18, 83 (1916) (in German)
• [2] H.B.G Casimir, Proc. K. Ned. Akad. Wet. 51, 635 (1948)
• [3] V.M. Mostepanenko, N.N. Trunov, The Casimir effect and its application (Claredon Press, Oxford, 1997)
• [4] R.L. Jaffe, Phys. Rev. D 72, 021301(R) (2005)
• [5] W. Pauli, In: N. Straumann (Ed.), Handbuch der Physik, Vol. XXIV (Springer-Verlag, Berlin, 1990) 202
• [6] N. Straumann, arXiv:gr-qc/0208027
• [7] S.E. Rugh, H. Zinkernagel, Stud. Hist. Philos. M. P. 33, 663, (2002) http://dx.doi.org/10.1016/S1355-2198(02)00033-3[Crossref]
• [8] V. Petrosian V, In: M.S. Longair (Ed.), Confrontation of Cosmological Theories with Observational Data (Dordrecht, D. Reidel Publishing, 1974) 63
• [9] A. Riess et al., Astron. J. 116, 1009 (1998) http://dx.doi.org/10.1086/300499[Crossref]
• [10] S. Perlmutter et al., Astrophys. J. 517, 565 (1999) http://dx.doi.org/10.1086/307221[Crossref]
• [11] S. Weinberg, Rev. Mod. Phys. 61, 1 (1989) http://dx.doi.org/10.1103/RevModPhys.61.1[Crossref]
• [12] S. Weinberg, arXiv:astro-ph/0005265
• [13] A.J.S. Capistrano, P.I. Odon, Apeiron 16, 3 (2009)
• [14] W. Chen, Y.S. Wu, Phys. Rev. D 41, 695 (1990) http://dx.doi.org/10.1103/PhysRevD.41.695[Crossref]
• [15] I. Waga, Astrophys. J. 414, 436 (1993) http://dx.doi.org/10.1086/173090[Crossref]
• [16] J.A.S. Lima, Braz. J. Phys. 94, 34 (2004)
• [17] S. Carneiro, M.A. Dantas, C. Pigozzo, J.S. Alcaniz, Phys. Rev. D 77, 083504 (2008) http://dx.doi.org/10.1103/PhysRevD.77.083504[Crossref]
• [18] T. Padmanabham, Gen. Relat. Gravit. 40, 529 (2008) http://dx.doi.org/10.1007/s10714-007-0555-7[Crossref]
• [19] S. Capozzielo, R. de Ritis, A.A. Marino, arXiv:grqc/9806043
• [20] M.S. Leszek, arXiv:gr-qc/0702097
• [21] R. Trotta, G. Starkman, AIP Conf. Proc. 878, 323 (2006) http://dx.doi.org/10.1063/1.2409104[Crossref]
• [22] J.M. Cline, H. Firouzjahi, AIP Conf. Proc. 646, 197 (2003) http://dx.doi.org/10.1063/1.1524573[Crossref]
• [23] S. Förste, Z. Lalak, S. Lavignac, H.P. Nilles, J. High Energy Phys. 0009, 034 (2000) http://dx.doi.org/10.1088/1126-6708/2000/09/034[Crossref]
• [24] S.H. Tye, I. Wasserman, Phys. Rev. Lett. 86, 1682 (2001) http://dx.doi.org/10.1103/PhysRevLett.86.1682[Crossref]
• [25] T. Padmanabhan, S. Shankaranarayanan, Phys. Rev. D 63, 105021 (2001) http://dx.doi.org/10.1103/PhysRevD.63.105021[Crossref]
• [26] Z. Kakushhadze, Phys. Lett. B 491, 317 (2000) http://dx.doi.org/10.1016/S0370-2693(00)01069-8[Crossref]
• [27] L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999) http://dx.doi.org/10.1103/PhysRevLett.83.3370[Crossref]
• [28] L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999) http://dx.doi.org/10.1103/PhysRevLett.83.4690[Crossref]
• [29] S. Tsujikawa, A.R. Liddle, ICAP 0403, 001 (2004)
• [30] S. Tsujikawa, M. Sami, R. Maartens, Phys. Rev. D 70, 063525 (2004) http://dx.doi.org/10.1103/PhysRevD.70.063525[Crossref]
• [31] M.D. Maia, arXiv:astro-ph/0404370v1
• [32] M.R. Nolta et al., Astrophys. J. Suppl. S. 180, 296 (2009) http://dx.doi.org/10.1088/0067-0049/180/2/296[Crossref]
• [33] P. Kanti, Phys. Rev. Lett. B 481, 386 (2000)
• [34] D. Langlois, M. Rodriguez-Martinez, Phys. Rev. D 64, 123507 (2001) http://dx.doi.org/10.1103/PhysRevD.64.123507[Crossref]
• [35] E.E. Flanagan et al., Phys. Lett. B 522, 155 (2001) http://dx.doi.org/10.1016/S0370-2693(01)01261-8[Crossref]
• [36] S. Jalalzadeh, H.R. Sepangi, Class. Quant. Grav. 22, 2035 (2005) http://dx.doi.org/10.1088/0264-9381/22/11/008[Crossref]
• [37] M. Heydari-Fard, M. Shirazi, S. Jalalzadeh, H.R. Sepangi, Phys. Lett. B 640, 1 (2006) http://dx.doi.org/10.1016/j.physletb.2006.07.020[Crossref]
• [38] M. Heydari-Fard, H. Razmi, H.R. Sepangi, Phys. Rev. D 76, 066002 (2007) http://dx.doi.org/10.1103/PhysRevD.76.066002[Crossref]
• [39] M. Heydari-Fard, H.R. Sepangi, Phys. Lett. B 649, 1 (2007) http://dx.doi.org/10.1016/j.physletb.2007.04.008[Crossref]
• [40] M. Heydari-Fard, H.R. Sepangi, Phys. Rev. D 76, 104009 (2007) http://dx.doi.org/10.1103/PhysRevD.76.104009[Crossref]
• [41] M.D. Maia, E.M. Monte, J.M.F. Maia, J.S. Alcaniz, Class. Quant. Grav. 22, 1623 (2005) http://dx.doi.org/10.1088/0264-9381/22/9/010[Crossref]
• [42] M.D. Maia, A.J.S. Capistrano, E.M. Monte, Int. J. Mod. Phys. A 24, 1545 (2009) http://dx.doi.org/10.1142/S0217751X09044978[Crossref]
• [43] P.I. Odon, A.J.S. Capistrano, Phys. Scripta 81, 045101 (2010) http://dx.doi.org/10.1088/0031-8949/81/04/045101[Crossref]
• [44] L. Schlaefli, Ann. di Mat. (2nd series) 5, 170 (1871)
• [45] J. Nash, Ann. Math. 63, 20 (1956) http://dx.doi.org/10.2307/1969989[Crossref]
• [46] R. Greene, Mem. Am. Math. Soc. 97, 1 (1970)
• [47] M.D. Maia, N. Silva, M.C.B. Fernandes, J. High Energy Phys. 0704, 047 (2007) http://dx.doi.org/10.1088/1126-6708/2007/04/047[Crossref]
• [48] M.D. Maia, A.J.S Capistrano, D. Müller, Int. J. Mod. Phys. D 18, 1273 (2009) http://dx.doi.org/10.1142/S0218271809015072[Crossref]
• [49] C.J. Isham, A. Salam, J. Strathdee, Phys. Rev. 3, 4 (1971)
• [50] J. Rosen, Rev. Mod. Phys. 37, 204 (1965) http://dx.doi.org/10.1103/RevModPhys.37.204[Crossref]
• [51] M.D. Maia, arXiv:0811.3835v1
• [52] M. Kowalski et al., Astrophys. J. 686, 749 (2008) http://dx.doi.org/10.1086/589937[Crossref]
• [53] M. Ozer, M.O. Taha, Phys. Lett. B 171, 363 (1986) http://dx.doi.org/10.1016/0370-2693(86)91421-8[Crossref]
• [54] W. Chen, Y.S. Wu, Phys. Rev. D 41, 695 (1990) http://dx.doi.org/10.1103/PhysRevD.41.695[Crossref]
• [55] J.L. Lopez, D.V. Nanopoulos, Mod. Phys. Lett. A 11, 1 (1996) http://dx.doi.org/10.1142/S0217732396000023[Crossref]
• [56] M.O. Calvão, Phys. Rev. D 45, 3869 (1962) http://dx.doi.org/10.1103/PhysRevD.45.3869[Crossref]
• [57] A.I. Arbab, A.M.M. Abdel-Rahman, Phys. Rev. D 50, 7725 (1994) http://dx.doi.org/10.1103/PhysRevD.50.7725[Crossref]
• [58] J. Bardeen, Phys. Rev. D 31, 1792 (1985) http://dx.doi.org/10.1103/PhysRevD.31.1792[Crossref]

Identyfikatory

DOI

10.2478/s11534-010-0046-4