TY - JOUR

T1 - Stability and attractor in a higher-dimensional cosmology. I

AU - Maeda, K.

PY - 1986/12/1

Y1 - 1986/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001094842&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001094842&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/3/2/017

DO - 10.1088/0264-9381/3/2/017

M3 - Article

AN - SCOPUS:0001094842

VL - 3

SP - 233

EP - 247

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 2

M1 - 017

ER -