Isotropization of scalar field Bianchi models with an exponential potential.

Abstract

We study whether homogeneous cosmological models containing a self-interacting scalar field with an exponential potential [of the form V(\ensuremath{\varphi})=\ensuremath{\Lambda}${\mathit{e}}^{\mathit{k}\mathrm{\ensuremath{\varphi}}}$] isotropize. Following Heusler [M. Heusler, Phys. Lett. B 253, 33 (1991)], we show that Bianchi models, other than possibly those of types I, V, VII, or IX, cannot isotropize if ${\mathit{k}}^{2}$>2. In this case we note that the solutions of Feinstein and Ib\'a\~nez [A. Feinstein and J. Ib\'a\~nez, Class. Quantum Grav. 10, 93 (1993)], which are neither isotropic nor inflationary, act as stable attractors. When ${\mathit{k}}^{2}$2 the cosmic no-hair theorem of Kitada and Maeda [Y. Kitada and K. Maeda, Phys. Rev. D 45, 1416 (1992); Class. Quantum Grav. 10, 703 (1993)] applies and the isotropic power-law inflationary FRW solution is the unique attractor for any initially expanding Bianchi model.