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We invesstigate thoroughly the dynamics of an inflation-driving scalar field in terms of an extended version of the stochastic approach proposed by Starobinsky and discuss the spacetime structure of the inflationary universe. To avoid any complications which might arise due to quantum gravity, we concentrate our discussion on the new inflationary universe scenario in which all the energy scales involved are well below the Planck mass. The investigation is done both analytically and numerically. In particular, we present a full numerical analysis of the stochastic scalar field dynamics on the phase space. Then implications of the results are discussed.
Nakao et al. (Thu,) studied this question.
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