A `dark-energy-free` turbulence 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(t). It grows linearly with gravitational time t, but exponentially with atomic clock (or proper) time,  τ = \int_0^t dt' / δ(t').   The resulting Ricci tensor is identically zero, so there is no critical density criterion.  The energy density is shown to decrease by a factor of 10¹²⁰ from the quantum field BIG BANG estimate (the so-called `Worst prediction in the history of physics') to the currently measured values.  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 all 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. This theory suggests strongly that it is not.

        

        [1]  www.turbulence-online.com/Publications/Purdue_April_2022_Paper.pdf