It is shown how the field equations for a self-interacting scalar field propagating in the Bianchi I spacetime can be expressed as a set of first-order non-linear partial differential equations. These equations are solved for (a) an exponential potential, and (b) a general potential when slow-roll is valid. It is shown how these solutions can be used to study anisotropic inflation in the Brans-Dicke theory of gravity and inflation driven by superstrings.
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James E. Lidsey (1992) studied this question.
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