This new theory is a published already theory of Einstein known as general relativity. If you admit the conservation of energy (which is built into Einstein gravitation in a form of vanishing divergence of stres-energy tensor) then for a static space you get the Hubble resdshift roughly as observed for the density of matter in space roughly as observed. You may calculate it easily and exactly with Newtonian approximation of GR since it may be done for space with weak gravitational field and slow matter. If you do you'll see how it simulates the accelerating expansion, with observed acceleration, and that the dynamical friction of photons was never before calculated exactly. It was just assumed to be negligible
by inventors of the Big Bang hypothesis to provide for their idea of expanding universe. Similarly the stuff about stability (note that we don't know how to solve 3 body problem, and the universe contains even more than 300 bodies, so how we can tell that this system is unstable?)
Regretable we can't write about Einstein's GR in a mainstream thread because certain calculations were neglected and now we need to pretend that we all believe that they were done and Einstein's universe was falsified. Have you ever seen the proof that there is no Hubble redshift in Einstein's universe (while energy is conserved) and that photons fly in it without any redshift
while everything else, including space probes (eg. Pioneers 10 ans 11) have this redshift?