We study the dynamics of a homogeneous, anisotropic, spatially flat universe filled with a scalar field minimally coupled to gravity. It turns out that in the general case the dynamical system possesses three Noether symmetries and when the potential of the scalar field is constant an additional, fourth symmetry appears. In this case the dynamical equations can be explicitly integrated. We study the properties of this class of solutions. For the generic potential anisotropy prevents early inflation, but inflation may appear at a later stage when anisotropy becomes much weaker.

• Received 30 January 1992

DOI:https://doi.org/10.1103/PhysRevD.46.1391