On the stochasticity in relativistic cosmology

I. M. Khalatnikov, E. M. Lifshitz, K. M. Khanin, L. N. Shchur, Ya G. Sinai

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Abstract

It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.(1) In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.

Original languageEnglish (US)
Pages (from-to)97-114
Number of pages18
JournalJournal of Statistical Physics
Volume38
Issue number1-2
DOIs
StatePublished - Jan 1 1985
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Stochastization
  • cosmological models
  • singularity

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    Khalatnikov, I. M., Lifshitz, E. M., Khanin, K. M., Shchur, L. N., & Sinai, Y. G. (1985). On the stochasticity in relativistic cosmology. Journal of Statistical Physics, 38(1-2), 97-114. https://doi.org/10.1007/BF01017851