Finite Action Principle Revisited

Abstract

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 δ\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.

arXiv comment14 pages, no figures or tables. Amended title, additions to introduction, conclusions, section 2.3 and refs. To appear in Phys. Rev. D

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