Stability and attractor in a higherdimensional cosmology. I
Abstract
The stability condition of (the fourdimensional Friedmann universe) x (a compact internal space) (F exp 4 x K exp D) is presented for a class of higherdimensional theories, in which the effective potential depends only on a scale length of the internal space. The CandelasWeinberg model (i.e. oneloop quantum correction plus a cosmological constant Lamda), elevendimensional supergravity plus Lambda, EinsteinYangMills theory and sixdimensional EinsteinMaxwell 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 nonlinear 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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 March 1986
 DOI:
 10.1088/02649381/3/2/017
 Bibcode:
 1986CQGra...3..233M
 Keywords:

 Big Bang Cosmology;
 SpaceTime Functions;
 Strange Attractors;
 Systems Stability;
 Unified Field Theory;
 Dynamical Systems;
 Gravitation Theory;
 Perturbation Theory;
 Potential Theory;
 Quantum Theory;
 Relativity;
 YangMills Theory;
 Astrophysics