In recent astrophysical literature there are splashs of acute discussions on the interpretation of the observed cosmological redshift: is it space expansion, the Doppler effect of receeding galaxies or the gravitational effect of cosmologically distributed matter. The question is how to distinctly observe these different interpretations of observed properties of cosmological redshift.
The problem was formulated by H.Bondi (1947) and also by E. Harrison in his book “Cosmology”, Cambridge Univ. Press, 1981 (second ed. 2000). Now there are more than ten papers which argue the different possibilities. Abramowicz et al.(2007; 2008) demonstrate that only space expansion can be used for understanding the cosmological redshift within general relativity, while Chodorowski (2007; 2011), Bunn & Hogg (2009), Melia (2012) insists on the interpretation as the sum of the Doppler effect plus the gravitational effect.
In general relativity space / space-time itself has the same level of existence as matter (Einstein equation joins them) so the space can be curved, stretch, spread (as gravitational waves) and so on. And this also can be considered as an argument in favor of the expanding space interpretation, though the problem is still open.