Up until recently I was fairly sure that the universe is expanding, i.e. the (spatial) metric is changing proportionally to the scale factor, such that the distance measured between objects is increasing over time. However I read this article and it has really made me doubt my understanding. So, I'd really like to clear my doubt up. Is the universe actually expanding (in the sense that the observational data agrees with the hypothesis that the universe is expanding), or is something else going on (from what I've read, a large number of scientists do think that the universe is expanding, and at an accelerated rate)?
The aforementioned article essentially states that we should not conclude that the universe is expanding due to the wavelength of photons being stretched (N.B the author considers an FRW universe in their analysis), since the wavelength of photon is not a property of the photon, but of the "photon + observer" system, thus whilst observers in a comoving FRW reference frame will observe a photons wavelength being stretched and hence observe it redshifting, those in a locally flat inertial reference frame at each point along the trajectory of a comoving observer will just observe this as a series of Doppler shifts.
The author states that expansion of space only has meaning to observers in a comoving reference frame relative to the expansion of the FRW metric and hence one should not conclude that the space is expanding, since, with an appropriate change of coordinates, the expanding of space [as an explanation for the change of wavelength of a photon] can be extinguished and replaced with the simple Doppler shift.
At least this is the gist that I got from it (I may very well have misinterpreted it though)!