  The main purpose of this paper is to advance a unified theory of dark matter,
dark energy, and inflation first formulated in 2008. Our minimal affine
extension of the GR has geodesics coinciding with the pseudo Riemannian ones,
up to parameterizations. It predicts a `sterile' massive vecton and depends on
two new dimensional constants, which can be measured in the limit of small
vecton velocity. In a special gauge, this velocity has an upper limit near
which it grows to infinity. The linearized vecton theory is similar to the
scalar models of inflation except the fact of internal anisotropy of the
vecton. For this reason we study general solutions of scalar analogs of the
vecton theory without restricting the curvature parameter and anisotropy by
using previously derived exact solutions as functions of the metric. It is
shown that the effects of curvature and anisotropy fast decrease in expanding
universes. Our approach can be applied to anisotropic universes, which is
demonstrated on an exactly solvable strongly anisotropic cosmology. To
characterize different cosmological scenarios in detail we introduce three
characteristic functions, two of which are small and almost equal during
inflation and grow near the exit. Instead of the potential it is possible to
use one of the two characteristic functions. This allows to approximately
derive flat isotropic universes with `prescribed' scenarios, which is the
essence of our constructive cosmology of early universes. The most natural
application of our approach is in analytically constructing characteristic
functions of inflationary models with natural exits. However, the general
construction can be applied to other problems, e.g., to evolution of
contracting universes.

General Relativity and Quantum Cosmology;High Energy Physics - Theory