An alternative cosmological model for an expanding universe

A model of an infinite universe is postulated in which both space and time expand together and are scaled by a time-dependent length scale, δ ( t ) . The Ricci tensor and Ricci scalar both vanish identically, so the Einstein field equations reduce to a balance between the time-dependent spatially averaged stress energy tensor T μ ν and its scalar invariant T / 2 times the metric tensor. The divergence of T μ ν − T g μ ν / 2 is zero, so the conserved quantity is G * = ρ c 2 / G δ 2 ( t ) , where c is the speed of light, ρ is the rest mass density, and G * is Quantum field theory prediction—the so-called “worst prediction in the history of physics.” The implications of this single time-dependent length scale hypothesis for our physical space are explored using the rules of tensor analysis. These imply that the length scale grows linearly with t which itself varies exponentially with atomic clock time. The Hubble parameter is just H ( t ) = 1 / t , where t is the age of the universe, so the universe expansion rate is slowing down. The Hubble parameter can be expressed in terms of the red-shift parameter z as H ( z ( t ) ) = H o [ 1 + z ] , where H o is its current value. H o = 63.6 km/s/Mpc is in excellent agreement with a large number of observations and implies that the universe began 15.4 × 10⁹ years ago. Excellent agreement is demonstrated by recent astronomical measurements with neither dark matter nor dark energy.