Mathematics – Dynamical Systems
Scientific paper
Mar 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cqgra...3..233m&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 3, March 1, 1986, p. 233-247.
Mathematics
Dynamical Systems
63
Big Bang Cosmology, Space-Time Functions, Strange Attractors, Systems Stability, Unified Field Theory, Dynamical Systems, Gravitation Theory, Perturbation Theory, Potential Theory, Quantum Theory, Relativity, Yang-Mills Theory
Scientific paper
The stability condition of (the four-dimensional Friedmann universe) x (a compact internal space) (F exp 4 x K exp D) is presented for a class of higher-dimensional theories, in which the effective potential depends only on a scale length of the internal space. The Candelas-Weinberg model (i.e. one-loop quantum correction plus a cosmological constant Lamda), eleven-dimensional supergravity plus Lambda, Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F exp x K exp D solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. It is found that the stable F exp 4 x K exp D solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.
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