Unobserved frequency shifts induced by random motion of gravitating masses on the expansion of a light beam

According to General Relativity, the large scale structures of the Universe can influence a light beam remotely by their gravitational fields, resulting in a gradual systematic ‘expansion’ of the beam which reflects the curvature of space. We show that if such an effect is present, any random speed v in the masses will cause the frequency ωo of the arriving extragalactic light to deviate slightly from its usual redshifted value, by an amount δωo/ωo ∝ ΩmL2v, where Ωm ∼ 0.3 is the total density of the various mass concentrations, L ∼ a few Gpc is the length of the light path, and v ∼ 300 km s is the mean random speed of the masses transverse to the beam. This is the first time frequency shifts arising from a dynamic Universe are calculated in the context of ‘expansion’. Previous attempts dealt with the much smaller effect when light is deflected by moving lenses the so-called ‘shear’ action on the beam. The actual magnitude and sign of the δωo presented here is fixed along a particular light path (because the phase space distribution of the masses varies slowly), but can differ between two widely separated light paths that sample independent mass distributions. Since the first epoch of star formation was at z ≈ 6 (before which the Universe was probably too smooth to affect the light frequency in the manner described), a conservative estimate of the effect for radiation emitted at z > 6 yields an average δωo/ωo ≈ 10, i.e. larger than the most prominent spatial temperature variation in the microwave background the first acoustic peak which is already well explained as a separate phenomenon. We are therefore led to the conclusion that the global propagation of light is not governed by the General Relativity theory in its present form.