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The dynamics of any spherical cosmology with a scalar field (`scalaron')coupling to gravity is described by the nonlinear second-order differentialequations for two metric functions and the scalaron depending on the `time'parameter. The equations depend on the scalaron potential and on the arbitrarygauge function that describes time parameterizations. This dynamical system canbe integrated for flat, isotropic models with very special potentials. But,somewhat unexpectedly, replacing the `time' variable by one of the metricfunctions allows us to completely integrate the general spherical theory in anygauge and with apparently arbitrary potentials. The main restrictions on thepotential arise from positivity of the derived analytic expressions for thesolutions, which are essentially the squared canonical momenta. An interestingconsequence is emerging of classically forbidden regions for these analyticsolutions. It is also shown that in this rather general model the inflationarysolutions can be identified, explicitly derived, and compared to the standardapproximate expressions. This approach can be applied to intrinsicallyanisotropic models with a massive vector field (`vecton') as well as to somenon-inflationary models.

A fresh view of cosmological models describing very early Universe: general solution of the dynamical equations