The equations of conformal cyclic cosmology. (English) Zbl 1317.83113
Summary: I review the equations of Conformal Cyclic Cosmology given by R. Penrose [Cycles of time. An extraordinary new view of the universe. London: Bodley Head (2010; Zbl 1222.00011)]. Motivated by the example of FRW cosmologies, I suggest a slight modification to Penrose’s prescription and show how this works out for Class A Bianchi cosmologies, and in general.
MSC:
| 83F05 | Relativistic cosmology |
| 53Z05 | Applications of differential geometry to physics |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 83C75 | Space-time singularities, cosmic censorship, etc. |
Citations:
Zbl 1222.00011References:
| [1] | Anderson, M.T.: Canonical metrics on 3-manifolds and 4-manifolds. Asian J. Math. 10, 127-163 (2006) · Zbl 1246.53063 · doi:10.4310/AJM.2006.v10.n1.a8 |
| [2] | Anguige, K.: Isotropic cosmological singularities. III. The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations. Ann. Phys. 282, 395-419 (2000) · Zbl 0973.83042 · doi:10.1006/aphy.2000.6037 |
| [3] | Anguige, K., Tod, K.P.: Isotropic cosmological singularities. I. Polytropic perfect fluid spacetimes. Ann. Phys. 276, 257-293 (1999) · Zbl 1003.83027 · doi:10.1006/aphy.1999.5946 |
| [4] | Anguige, K., Tod, K.P.: Isotropic cosmological singularities. II. The Einstein-Vlasov system. Ann. Phys. 276, 294-320 (1999) · Zbl 1003.83028 · doi:10.1006/aphy.1999.5947 |
| [5] | Fefferman, C., Graham, C.R.: The Ambient Metric. Annals of Mathematics Studies, vol. 178. Princeton University Press, Princeton (2012) · Zbl 1243.53004 |
| [6] | Friedrich, H.: On purely radiative space-times. Commun. Math. Phys. 103, 35-65 (1986) · Zbl 0584.53038 · doi:10.1007/BF01464281 |
| [7] | Friedrich, H.: On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations. J. Differ. Geom. 34, 275-345 (1991) · Zbl 0737.53070 |
| [8] | Lee, J.M., Parker, T.H.: The Yamabe problem. Bull. Am. Math. Soc. 17, 37-91 (1987) · Zbl 0633.53062 · doi:10.1090/S0273-0979-1987-15514-5 |
| [9] | Lübbe, C.: Conformal scalar fields, isotropic singularities and conformal cyclic cosmologies. arXiv:1312.2059 · Zbl 0584.53038 |
| [10] | Lübbe, C., Kroon, J.A.V.: A conformal approach for the analysis of the non-linear stability of radiation cosmologies. Ann. Phys. 328, 1-25 (2013) · Zbl 1263.83188 · doi:10.1016/j.aop.2012.10.011 |
| [11] | Newman, E.T.: A Fundamental Solution to the CCC equation. arXiv:1309.7271 · Zbl 1291.83051 |
| [12] | Penrose, R.: Cycles of Time: An Extraordinary New View of the Universe. Bodley Head, London (2010) · Zbl 1222.00011 |
| [13] | Penrose, R., Rindler, W.: Spinors and Space-Time, Volume 1: Two-Spinor Calculus and Relativistic fields. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge (1987) · Zbl 0663.53013 |
| [14] | Rendall, A.D.: Asymptotics of solutions of the Einstein equations with positive cosmological constant. Ann. Henri Poincar 5, 1041-1064 (2004) · Zbl 1061.83008 · doi:10.1007/s00023-004-0189-1 |
| [15] | Starobinsky, A.A.: Isotropization of arbitrary cosmological expansion given an effective cosmological constant. JETP Lett. 37, 66-69 (1983) |
| [16] | Tod, K.P.: Isotropic cosmological singularities in spatially homogeneous models with a cosmological constant. Class. Quantum Grav. 24, 2415-2432 (2007) · Zbl 1115.83023 · doi:10.1088/0264-9381/24/9/017 |
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