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 Tμν and its scalar invariant T/2 times the metric tensor. The divergence of Tμν−Tgμν/2 is zero, so the conserved quantity is G*=ρc2/Gδ2(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))=Ho[1+z], where Ho is its current value. Ho=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.