Figure. 2a. Plot showing successive exponential expansions of type r(t) = exp(t - t_0) -1 (green) for different (past) values of t₀ ≥ 0, together with the trajectory of a light ray (red) through the present (defined as r = 0, t = 0). The choice of r = 0 and t = 0 as the present is arbitrary; it is a property of the exponential function that the curves would look the same if plotted for any other r and t chosen to define the present. (To the observer, both space and time appear subjected to exponential transformation ). b. Detail of Figure 2a around t = -1 and r = -1 showing how the set of exponential functions in Figure 2a seemingly form an essentially horizontal set of lines parallel to the t-axis, with decreasing separation for successively more distant r from the observer at r = 0 and piling up at r = -1. This property of exponential functions is important for the formation of a Planck spectrum as is illustrated in Figure 5 below

From

Is CMB just an Observational Effect of a Universe in Accelerated Expansion?

Arne Bergstrom

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