×

The deformable universe. (English) Zbl 1228.83139

Summary: The concept of smooth deformations of Riemannian manifolds, recently evidenced by the solution of the Poincaré conjecture, is applied to Einstein’s gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.

MSC:

83F05 Relativistic cosmology
53Z05 Applications of differential geometry to physics
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
85A40 Astrophysical cosmology
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Arkani-Hamed N. et al.: Phys. Lett. B 429, 263 (1998) · Zbl 1355.81103 · doi:10.1016/S0370-2693(98)00466-3
[2] Rubakov V.A., Shaposhnikov M.: Phys. Lett. B 125, 136 (1983) · doi:10.1016/0370-2693(83)91253-4
[3] Randall L., Sundrum R.: Phys. Rev. Lett. 83, 3370 (1999) · Zbl 0946.81063 · doi:10.1103/PhysRevLett.83.3370
[4] Randall L., Sundrum R.: Phys. Rev. Lett. 83, 4690 (1999) · Zbl 0946.81074 · doi:10.1103/PhysRevLett.83.4690
[5] Dvali G., Gabadadze G., Porrati M.: Phys. Lett. B 485, 208 (2000) · Zbl 0961.83045 · doi:10.1016/S0370-2693(00)00669-9
[6] Sahni V., Shtanov Y.: IJMP D 11, 1515 (2002) · Zbl 1062.83555 · doi:10.1142/S0218271802002827
[7] Sahni V., Shtanov Y.: JCAP 0311, 014 (2003) · doi:10.1088/1475-7516/2003/11/014
[8] Shiromizu T., Maeda K., Sasaki M.: Phys. Rev. D 62, 024012 (2000) · doi:10.1103/PhysRevD.62.024012
[9] Dick R.: Class. Quant. Grav. 18, R1 (2001) · Zbl 0996.83001 · doi:10.1088/0264-9381/18/17/201
[10] Hogan C.J.: Class. Quant. Grav. 18, 4039 (2001) · Zbl 0992.83110 · doi:10.1088/0264-9381/18/19/310
[11] Deffayet C., Dvali G., Gabadadze G.: Phys. Rev. D 65, 044023 (2002) · doi:10.1103/PhysRevD.65.044023
[12] Alcaniz J.S.: Phys. Rev. D 65, 123514 (2002) · doi:10.1103/PhysRevD.65.123514
[13] Jain D., Dev A., Alcaniz J.S.: Phys. Rev. D 66, 083511 (2002) · doi:10.1103/PhysRevD.66.083511
[14] Lue A.: Phys. Rep. 423, 1 (2006) · doi:10.1016/j.physrep.2005.10.007
[15] Heydari-Fard M., Shirazi M., Jalalzadeh S., Sepangi H.R.: Phys. Lett. B 640, 1 (2006) · doi:10.1016/j.physletb.2006.07.020
[16] Goenner H.F.: Ann. Phys. 522, 389 (2010) · Zbl 1195.83103 · doi:10.1002/andp.201010450
[17] Riemann, B.: On the Hypothesis That Lie at the Foundations of Geometry (1854), translated by W. K. Clifford, Nature, 8,114 (1873) · JFM 05.0230.03
[18] Pesic, P.: Beyond Geometry, Dover, New York (2007) · Zbl 1152.01300
[19] Misner C.W., Thorne Kip S., Wheeler John A.: Gravitation. W. H. Freeman Co, New York (1970)
[20] Schlaefli, L.: Annali di Matatematica, 2nd series. 5, 170–193 (1871)
[21] Eisenhart L.P.: Riemannian Geometry. Pinceton U. P., (1966)
[22] Nash J.: Ann. Math. 63, 20 (1956) · Zbl 0070.38603 · doi:10.2307/1969989
[23] York J.W. Jr: Phys. Rev. Lett. 26, 1656 (1971) · doi:10.1103/PhysRevLett.26.1656
[24] Hamilton R.: J. Differ. Geom. 17, 255 (1982)
[25] Perelman, G.: arXiv:math/0211159
[26] Buchert T., Carfora M.: Class. Quantum Gravity 19, 6109 (2002) · Zbl 1021.83028 · doi:10.1088/0264-9381/19/23/314
[27] Maia M.D., Silva N., Fernandes M.C.B.: JHEP 047, 0704 (2007)
[28] Crampin M., Pirani F.A.E.: Applicable Differential Geometry. Cambridge University Press, Cambridge (1986) · Zbl 0606.53001
[29] Maia M.D., Monte E.M., Maia J.M.F., Alcaniz J.S.: Class. Quant. Grav. 22, 1623 (2005) · Zbl 1070.83543 · doi:10.1088/0264-9381/22/9/010
[30] Maia M.D., Monte E.M., Maia J.M.F.: Phys. Lett. B 585, 11 (2004) · Zbl 1246.83261 · doi:10.1016/j.physletb.2003.12.079
[31] Israel W.: Nuovo Cimento 44, 4349 (1966)
[32] Isham C.J., Salam A., Strathdee J.: Phys. Rev. 3, 4 (1971)
[33] Gupta S.N.: Phys. Rev. 96(6), 1683 (1954) · Zbl 0056.44103 · doi:10.1103/PhysRev.96.1683
[34] Fronsdal C.: Phys. Rev. D 18, 3624 (1978) · doi:10.1103/PhysRevD.18.3624
[35] Spergel D.N. et al.: Astrophys. J. Suppl. Ser. 170, 377 (2007) · doi:10.1086/513700
[36] Xu, L., et al. JCAP, 07, 031 (2009)
[37] Astier P. et al.: Astron. Astrophys. 447, 31 (2006) · doi:10.1051/0004-6361:20054185
[38] Padmanabhan T., Choudhury T.R.: Mon. Not. R. Astron. Soc. 344, 823 (2003) · doi:10.1046/j.1365-8711.2003.06873.x
[39] Silva P.T., Bertolami O.: Astrophys. J. 599, 829 (2003) · doi:10.1086/379362
[40] Zhu Z.H., Alcaniz J.S.: Astrophys. J. 620, 7 (2005) · doi:10.1086/427061
[41] Alcaniz J.S.: Phys. Rev. D 69, 083521 (2004) · doi:10.1103/PhysRevD.69.083521
[42] Choudhury T.R., Padmanabhan T.: Astron. Astrophys. 429, 807 (2005) · Zbl 1065.85513 · doi:10.1051/0004-6361:20041168
[43] Kowalski M. et al.: Astrophys. J. 686, 749 (2008) · doi:10.1086/589937
[44] Samushia L., Ratra B.: Astrophys. J. 650, L5 (2006) · doi:10.1086/508662
[45] Komatsu E. et al.: Astrophys. J. Suppl. 180, 330 (2009) · doi:10.1088/0067-0049/180/2/330
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.