Expanding space, redshifts, and rigidity: Conceptual issues in cosmology

I examine the interpretation of photon redshifts in curved spacetime, as being gravitational or Doppler in origin. In Friedmann-Lema\^itre-Robertson-Walker spacetime, redshifts between comoving observers are often attributed to "expanding space", whereas in Schwarzschild spacetime, redshifts between static observers are attributed to "gravitational" causes. Yet various authors have suggested a freely falling observer congruence would interpret any redshift as Doppler, whereas a rigid congruence must interpret it as gravitational since there is no relative motion. I realise this proposal by explicitly constructing coordinate systems for rigid motion in the above spacetimes. This includes an extensive analysis of observer-dependent distance measurement in curved spacetime. I also introduce Rindler acceleration, the Milne model, and Newtonian cosmology.