Finite Action Principle Revisited
  We extend the cosmological predictions from assuming the total action of the
universe is finite. When initial and final singularities in curvature
invariants are avoided, it leads to singularities in the gravitational action
of the universe. The following properties are required of a universe with
finite action: Compact spatial sections (ie a closed universe) giving a finite
total lifetime for the universe. Compactification of flat and open universes is
excluded. The universe can contain perfect fluids with -1<p/\r{ho}<2 on
approach to singularities. The universe cannot display a bounce' or indefinite
cyclic behaviour to the past or the future. We find new consequences of
imposing finite action: the universe cannot be dominated by massless scalar
fields, the kinetic energy of scalar fields, or a p=\r{ho} perfect fluid on
approach to the initial or final singularity The ekpyrotic scenario with an
effective fluid obeying p/\r{ho}>2 in a closed, flat or open universe is
excluded. Any bouncing model with indefinite past or future evolution is ruled
out. Einstein static and steady-state universes are ruled out along with past
or future eternal inflating universes. Anisotropies cannot dominate the
dynamics at singularities. This excludes density inhomogeneity spectra versus
mass, of the form {\delta}\r{ho}/\r{ho}proportional to M^{-q}, with
q>2/3.Higher-order lagrangian theories of gravity are constrained. The
Gauss-Bonnet combination causes an action singularity even though it does not
contribute terms to the field equations. Scalar-tensor theories dominated by
the scalar field on approach to singularities have action singularities. Dark
energy cannot be a cosmological constant. The dark energy must evolve in a
closed universe that collapses to a future singularity that cannot be dominated
by the kinetic energy of the scalar field.
