I Does expanding space cause cosmological redshift?

[p78653]

The cosmological redshift is generally assumed to be due to space expansion.

But if spacetime is locally flat Minkowskian then surely photon wavelength should not change?

 

[PeterDonis]

The cosmological redshift is generally assumed to be due to space expansion.

No, it isn't "assumed" to be due to anything. It is calculated to be due to the spacetime geometry of the universe and the relationship of the worldlines of light rays to the worldlines of comoving observers.

if spacetime is locally flat Minkowskian then surely photon wavelength should not change?

No, this is not correct. There is no such thing as "photon wavelength" independent of a particular observer measuring the photon, or more precisely "light ray" (since we are not talking about quantum physics here and "photon" is a quantum concept).

 

[Orodruin]

In addition to what was already said, in local Minkowski coordinates, comoving observers are not at relative rest - so they ahould experience a mutual redshift.

See: https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/

 

[Ibix]

But if spacetime is locally flat Minkowskian then surely photon wavelength should not change?

This statement is analogous to the claim that because the surface of the Earth is locally flat Euclidean great circle paths can't cross again. The key point is that "locally flat" is an approximation that is only exactly true over a region of zero size. Actually, curvature is negligible over a small region, but never totally absent.

In an ideal FLRW universe you and I could independently verify that we each see the CMB as isotropic. If we were megaparsecs apart then as soon as we could see each other we would be able to see redshift in each other. But if we were only a meter apart our redshift would be something like $10^{-18}$ - unmeasurably small. It'd be 140 million years before we were 1cm further apart (assuming us being over-dense can be neglected - in fact our gravitational attraction would overwhelm our expansion velocity on a timescale of fractions of a microsecond). It would be totally fine to ignore cosmological curvature over human time scales. Just as you don't bother accounting for the curvature of the Earth when you tile a floor, but you need to worry about it when planning a city.