A direct consequence of the Expansion of Space?

Consider radar ranging of a distant galaxy in a Friedman–Lemaître cosmological model. In this model the comoving coordinate of the galaxy is constant; hence, the equations of null geodesics for photons travelling to the distant galaxy and back implyHere, τ e , τ r and τ o are, respectively, the times of emission, reflection and observation of the reflected photons, and a (τ) is the scalefactor. Since the Universe is expanding, a (τ) is a monotonically increasing function, so the return traveltime, τ o −τ r , must be greater than the forward traveltime, τ r −τ e . Clearly, space expands, and on their way back, the photons must travel a longer distance! This paper explains why this argument for the Expansion of Space (EoS) is wrong. We argue that, unlike the expansion of the cosmic substratum, the EoS is unobservable. We therefore propose to apply to it – just like to the ether – Ockham's razor.