The sufficient connection is the symmetry of metric tensor of spacetime. If this metric is symmetric then in a stationary universe the photons have exactly zero redshift. It allows the cosmologists to assume that Hubble redshift is a result of the expansion of the universe (Doppler redshift). It contradicts though the conservation of energy that necessarily causes the dynamical friction of photons and a non vanishing value of redshift also in a stationary universe.

The mainstream cosmologists justify their assumption of non conservation of energy by assuming that it would have a "negligible" effect on redshift of photons in stationary universe. My calculations show that it would produce Hubble constant equal sqrt(4*pi*G*rho), where (G) is Newtonian gravitational constant and (rho) is density of the universe, which for the presently estimated density of the universe 2.6x10^-27kg/m^3 it would produce an illusion of accelerating expansion with Hubble constant H_o=46km/s/Mpc and dH/dt=-H_o^2/2. Surely neither a negligible value.

Furthermore, if the universe happened to be Einstein's (stationary) uiverse its illusion of expansion would have to be with Hubble constant H_o=c/R_E, where c is speed of light and R_E is "Einstein's radius of the universe" which migh have also some aesthetic value which cosmologists value so much in Einstein's gravitation despite that Einstein himself advised to leave the elegance to a tailor.