A new single-length-scale similarity solution for an infinite homogeneous expanding universe using Einstein's averaged field equations.

 A similarity solution is proposed [1] in which both time and space independent variables are scaled with a single time-dependent length scale, δ. It grows linearly with gravitational time t, but exponentially with atomic clock (or proper) time,  τ.   The resulting Ricci tensor is identically zero, so there is no critical density criterion.  The energy density is shown to have evolved by a factor of -120 orders of magnitude to the currently measured values from the quantum field BIG BANG estimate (the so-called `Worst Prediction in the History of Physics’).  There is no need for dark matter or dark energy.   The Hubble parameter is H/H_o=t_o / t = 1+z where t_o is the age of the universe and  z is the redshift. H_o =63.4 provides an excellent fit to the data, and corresponds to an age of the universe of 15.4 billion years.  Excellent agreement is also shown with the supernovae data, previously believed to imply the universe is accelerating.

1.  WK George and T.J Johansson (2022)  `An Alternative Cosmological Model for an Expanding Universe, {http://www.turbulence-online.com}