Regularization of the big bang singularity with random perturbations. (English) Zbl 1386.83097
Summary: We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result [B. Xue and E. Belbruno, Classical Quantum Gravity 31, No. 16, Article ID 165002, 17 p. (2014; Zbl 1298.83101)] that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.
MSC:
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 62P35 | Applications of statistics to physics |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 83F05 | Relativistic cosmology |
Citations:
Zbl 1298.83101References:
| [1] | Xue, B. K.; Belbruno, E., Class. Quantum Grav., 31, (2014) · Zbl 1298.83101 · doi:10.1088/0264-9381/31/16/165002 |
| [2] | Mohammed, S-E; Scheutzow, M., Ann. Probab., 27, 615, (1999) · Zbl 0940.60084 · doi:10.1214/aop/1022677380 |
| [3] | Belbruno, E., Capture Dynamics and Chaotic Motions in Celestial Mechanics, (2004), Princeton: Princeton University Press, Princeton · Zbl 1057.70001 |
| [4] | Garfinkle, D.; Lim, W. C.; Pretorius, F.; Steinhardt, P. J., Phys. Rev. D, 78, (2008) · doi:10.1103/PhysRevD.78.083537 |
| [5] | Erickson, J. K.; Wesley, D. H.; Steinhardt, P. J.; Turok, N., Phys. Rev. D, 69, (2004) · doi:10.1103/PhysRevD.69.063514 |
| [6] | Mukhanov, V., Physical Foundations of Cosmology, p 336, (2005), Cambridge: Cambridge University Press, Cambridge · Zbl 1095.83002 |
| [7] | Steinhardt, P. J.; Turok, N., Phys. Rev. D, 65, (2002) · doi:10.1103/PhysRevD.65.126003 |
| [8] | Lehners, J-L, Class. Quantum Grav., 28, (2011) · Zbl 1228.83136 · doi:10.1088/0264-9381/28/20/204004 |
| [9] | McGehee, R., Commentarii Math. Helvetici, 56, 527-557, (1981) · Zbl 0498.70015 · doi:10.1007/BF02566226 |
| [10] | Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, (2002), Berlin: Springer, Berlin |
| [11] | Belbruno, E., Celest. Mech. Dyn. Astron., 115, 21-34, (2013) · Zbl 1266.85006 · doi:10.1007/s10569-012-9449-4 |
| [12] | Xue, B.; Garfinkle, D.; Pretorius, F.; Steinhardt, P. J., Phys. Rev. D, 88, (2013) · doi:10.1103/PhysRevD.88.083509 |
| [13] | Kloeden, P. E.; Platen, E., Numerical Solution of Stochastic Differential Equations, (1992), Berlin: Springer, Berlin · Zbl 0925.65261 |
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.
