STABILITY AND ATTRACTOR IN KALUZA-KLEIN COSMOLOGY. 1.

The stability condition of (the four-dimensional Friedmann universe)*(a compact internal space) (F4*KD) 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+a cosmological constant Lambda ), eleven-dimensional supergravity+ Lambda , Einstein-Yang-Mills theory and six-dimensional Einstein-Maxwell theory are classified into this class. It is shown that the F4*KD solution is stable against small perturbations in the above models. The stability against non-linear perturbation is also investigated. The author finds that the stable F4*KD solution is an attractor for a finite range of initial conditions if the proper volume of the universe is increasing with time.

Kaluza-Klein model
FIELD EQUATIONS: SOLUTION
STABILITY
APPROXIMATION: EFFECTIVE POTENTIAL
PERTURBATION THEORY: HIGHER-ORDER
SUPERGRAVITY: ELEVEN-DIMENSIONAL
GAUGE FIELD THEORY: YANG-MILLS
Einstein-Maxwell equation
FIELD THEORY: SIX-DIMENSIONAL
Friedman model

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