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2013

Astronomical Redshifts and the Expansion of Space

Kaiser, Nick

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In homogeneous cosmological models the wavelength $\lambda$ of a photon exchanged between two fundamental observers changes in proportion to expansion of the space $D$ between them, so $\Delta\log(\lambda / D) = 0$.

This is exactly the same as for a pair of observers receding from each other in flat space-time where the effect is purely kinematic.
The interpretation of this has been the subject of considerable debate, and it has been suggested that all redshifts are a relative velocity effect, raising the question of whether the wavelength always stretches in proportion to the emitter-receiver separation.
Here we show that, for low redshift at least, $\Delta\log(\lambda / D)$ vanishes for a photon exchanged between any two freely-falling observers in a spatially constant tidal field, because such a field stretches wavelengths and the space between the observers identically.

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