Figures index

From

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

Arne Bergstrom

International Journal of Physics. 2013, 1(6), 133-137 doi:10.12691/ijp-1-6-1
  • Figure. 1a. Simulated received radiation energy P[x] accumulated (105 histories) from different directions x in a small region of the sky (with x = 0 … 10,000), and with closer sources assumed to be completely opaque to the radiation from more distant ones in the same direction. The corresponding spectrum is shown in Figure 1b to be essentially indistinguishable from an exact Planck spectrum. b. Energy spectrum S[ω] (suitably scaled, with ω = 10 … 100) accumulated (30105 histories) from the received radiation energy P[x] in Figure 1a. The sampled spectrum (black) is seen to be virtually indistinguishable from the Planck spectrum (red) also shown
  • Figure. 2a. Plot showing successive exponential expansions of type r(t) = exp(t - t0) -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
  • Figure. 3. The cumulative distribution function F(R, t0) in (6) as function of t0 for values of R = 1, 2, 3, 4…, illustrating that for values of R greater than R ≈ 5, the function F(R, t0) is well approximated by the function F(t0) = 1 – exp (-t0 ) in (7)
  • Figure. 4. Plot of the function F1 = -1 - ln(P)/1000 as in (9) [and for comparison F2 = -P1/1000 (coinciding)], illustrating that this function gives only a small variation in the value of r when P varies, which is the reason for the discussed piling-up at r = -1
  • Figure. 5. Sampled (108 histories) energy spectra S[ω] as in Figure 1b for A) a Gaussian distribution (galaxies transparent), B) a Planck distribution (galaxies opaque, exponentially accelerated expansion), and C) a Planck-type distribution with distorted tail (galaxies opaque, but no accelerated expansion)