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We study numerically the onset of inflation under inhomogeneous initial conditions for various inflationary scenarios and various initial parameters. We solve the full Einstein equations for the gravitational field coupled to scalar-field and radiation-field sources, under the assumptions of spherical symmetry and a closed-universe background. We find that a large initial inhomogeneity suppresses the onset of inflation, and that the scalar field must have values suitable for inflation over a region of several horizon sizes for the inflationary phase to begin.
Goldwirth et al. (Mon,) studied this question.