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.
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