Cosmology of Spin-2 Fields
  The Cauchy-Kowalevski theorem is applied to the solutions of Einstein's
equations and to cosmology. Three fundamental requirements of the theorem: the
use of analytic series; the existence of the boundary surfaces; and the setting
of the independent initial data are revised, using methods of geometric
analysis. It is shown that during its relativistic phase, the standard model of
the universe is governed by Einstein's gravitation described as a massless
spin-2 field, but it is necessarily complemented by massive spin-2 field, which
responds for the dark sector of the universe. On the other hand, at the
inflationary phase, the exponential growth of the volume of the universe is
shown to be consistent with a thermal, non-relativistic expansion. These two
phases are separated by the last inflationary surface.
