The idea of the stationary Universe arose in physics in the middle of the 20th century in connection with comprehension of that circumstance that the found red shift in ranges of remote galaxies can be explained not only resorting to a Doppler effect and a hypothesis of the Big Bang.
As example the model developed in 1948 by Fred Hoil, Thomas Gold, German Bondi, etc. According to this model can serve, in process of Universe expansion between scattering galaxies the new matter constantly is created. Thus the cosmological principle is kept. The model had quite larger support in the 50th - the 60th years. Opening of relict radiation led number of her supporters to sharp decrease.
Now the field theory of elementary particles established the mechanism of loss by photons of a part of energy at their passing through the Universe the alternate to a Doppler effect and a hypothesis of the Big Bang. - It is a photon-neutrino interaction ignored by standard model. Thus the idea of the stationary Universe got unexpected support and consequently now it can't be dismissed. After all it can appear that the Universe doesn't extend at all - anybody counter yet didn't prove.