Nonsingular Einsteinian Cosmology: How Galactic Momentum Prevents Cosmic Singularities

It is shown how Einstein's equation can account for the evolution of the universe without an initial singularity and can explain the inflation epoch as a momentum dominated era in which energy from matter and radiation drove extremely accelerated expansion of space. It is shown how an object with momentum loses energy to the expanding universe and how this energy can contribute to accelerated spatial expansion more effectively than vacuum energy, because virtual particles, the source of vacuum energy, can have negative energy, which can cancel any positive energy from the vacuum. Radiation and matter with momentum have positive but decreasing energy in the expanding universe, and the energy lost by them can contribute to accelerated spatial expansion between galactic clusters, making dark energy a classical effect that can be explained by general relativity without quantum mechanics, and, as (13) and (15) show, without an initial singularity or a big bang. This role of momentum, which was overlooked in the Standard Cosmological Model, is the basis of a simpler model which agrees with what is correct in the old model and corrects what is wrong with it. 1. Introduction The Standard Cosmological Model entails a space-time metric with line element [1–4] where is the vacuum speed of light relative to a local Lorentz frame, is cosmic time, is the time-dependent scale factor of the Universe, and , , are spherical coordinates of a spatially flat (Euclidean) 3-space. A particle of proper mass has the Hamiltonian [5, 6] where , , and are canonical momenta conjugate to canonical coordinates , , and , respectively. The azimuthal angular momentum is conserved because does not depend on , but is not conserved unless all three momenta vanish. If , the polar angular momentum is conserved because no longer depends on . If , the radial momentum is conserved because no longer depends on . Defining , then reduces to showing how a particle with momentum loses energy to the expanding Universe [5]. A logical question, then, is where does that energy go? A logical answer is that it goes to the Hamiltonian of the Universe, which, in a one-dimensional minisuperspace model, can be expressed in geometrized units as the conserved quantity [7] with canonical momentum , canonical coordinate , effective mass , and potential where is the spatial curvature constant (±1 or 0), is a constant such that , is Einstein’s cosmological constant, and are energy densities of matter and radiation, respectively, at some initial time , and . The first term of is eliminated by metric (1), for which .