http://arxiv.org/abs/1912.12926
We evaluate the cosmological predictions that can be made assuming that 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. A universe with finite action must have compact spatial sections giving a finite total lifetime. Compactification of flat and open universes is excluded. The universe cannot be dominated by massless scalar fields or the kinetic energy of self-interacting scalar fields or a p=\r{ho} perfect fluid on approach to the initial or final singularity 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. The ekpyrotic scenario with an effective fluid obeying p/\r{ho}>2 is excluded. Bouncing loop quantum gravity models are ruled out. The Einstein static and steady-state universes are excluded along with past or future eternal inflating universes. Anisotropies cannot dominate the dynamics on approach to singularities. Higher-order lagrangian theories of gravity are significantly constrained. Quadratic lagrangians with fluids satisfying p/\r{ho}>-1/3 are excluded. The Gauss-Bonnet term causes an action singularity despite not contributing terms to the field equations. Scalar-tensor theories like Brans-Dicke dominated by the scalar field on approach to singularities have action singularities. Dark energy cannot be a simple cosmological constant, as it would create an action singularity to the future. The dark energy must be an evolving energy density in a closed universe that produces collapse to a future singularity.
J. Barrow
Wed, 1 Jan 20
27/88
Comments: 14 pages, no figures or tables