Abstract
We find the exact general solution for cosmological models arising from the interaction of the gravitational field with two scalar fields in both flat Robertson - Walker and the locally rotationally symmetric Bianchi I spacetime filled with an exponential potential. One scalar field self-interacts with this potential and the other is a free massless scalar field. The solutions have a singularity and a set of these exhibit the transition to power-law inflation for both metrics.
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