We reconsider and extend the cosmological predictions that can be made under the assumption 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. The following properties are required of a universe with finite action: Compact spatial sections (i.e., 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/ρ<2 on approach to singularities. The Universe cannot display a bounce or indefinite cyclic behavior to the past or the future. Here, we establish new consequences of imposing finite action: the Universe cannot be dominated by massless scalar fields or the kinetic energy of self-interacting scalar fields or a p=ρ perfect fluid on approach to the initial or final singularity. The ekpyrotic scenario with an effective fluid obeying p/ρ>2 in a closed, flat or open universe is excluded. Any bouncing loop quantum gravity model with indefinite past or future evolution is ruled out. The Einstein static and steady-state universes are ruled out along with past or future eternal inflating universes anisotropies of Kasner or Mixmaster type cannot dominate the dynamics on approach to singularities. This excludes density inhomogeneity spectra versus mass, of the form δρ/ρ∝M−q, with q>2/3. Higher-order Lagrangian theories of gravity are significantly constrained. Quadratic Lagrangians are excluded with fluids satisfying p/ρ>−1/3. Lagrangians with Lg=R1+δ have infinite actions on approach to a singularity when 2δ(1−3γ)+2−3γ<0, where p=(γ−1)ρ for the fluid. As shown by Barrow and Tipler, the Gauss-Bonnet quadratic combination causes a cosmological action singularity even though it does not contribute 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 Universe cannot be asymptotically de Sitter as t→∞. The dark energy must be an evolving energy density in a closed universe that produces collapse to a future singularity and cannot be dominated by the kinetic energy of the scalar field.