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The redshift and apparent luminosity of any given galaxy are not constant with time for most models of the expanding universe. Redshifts decrease with time because of the braking action of the gravitational field in all exploding models, except for the one where the matter density is zero. Apparent luminosities decrease with time, except for the oscillating model in the contracting phase and for galaxies with very large Δλ/λ0 values, because the distances between galaxies are increasing Redshifts increase with time for every galaxy in the steady-state model. The theory and numerical results of the deceleration are presented for four selected world models. For a galaxy with redshift z = Δλ/λ0 = 0.4 at the present epoch, the change of redshift with time is found to be dcz/dt = -11 X 10-6 km/sec year for the oscillating model in the expanding phase at qo = +1; dcz/dt = - 5.9 X 10-6 km/sec year for the Euclidean model; dcz/dt = -4.3 X 10-6 km/sec year for the hyperbolic model at qo = 0.3516; and dcz/dt = +9.2 X 10-6 km/sec year for the steady-state model. These all assume that H-1 = 13 X 109 years at the present epoch With present optical techniques there is apparently no hope of detecting such small changes in redshift for time intervals smaller than 10 years. If radio techniques are used with observation of the 21-cm H I line, the detection of a frequency shift of 3 X 10-2 cycles/sec year is required for the quoted deceleration of the oscillating case, which again appears to be impossible with present methods.
Allan Sandage (Sat,) studied this question.