The CMB spectrum shows the intensity of fluctuation at a certain angular scale:

Power spectrum

The achievement is the correspondence between the predicted power spectrum and the observed one.

My question is as follows:

Isn't the prediction terribly dependent on the initial conditions/the pattern of acoustic oscillations at that exact moment? Since the maxima correspond to modes caught, at that particular moment, at their oscillation extrema.


1 Answer 1


The CMB temperature anisotropy power spectrum was not formed in an instant.

Below is a plot of the photon visibility function (V) as a function of redshift (z). (The visibility function V(z) is the probability that a CMB photon was last scattered in the redshift interval, here normalized to have a maximum of 1.)

The photons from the photosphere of last scatter were scattered primarily from z=900 to z=1200. In terms of time, the half-width of the visibility function is 115,000 years.

Even after the epoch of last scattering, there are some photons that have been scattered again, although most have not.

So the CMB temperature anisotropy power spectrum is primarily reflective of the conditions during the z=900 to z=1200 time period.

enter image description here

  • $\begingroup$ I know this is an old answer, but could I ask from where did you obtained the plots or the data? $\endgroup$
    – Javier
    Aug 10, 2018 at 17:33
  • 1
    $\begingroup$ @Javier It is Fig. 3 from this paper. aanda.org/articles/aa/full/2006/04/aa3988-05/… Not my work. "Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination" A&A 446, 39-42 (2006). $\endgroup$
    – DavePhD
    Aug 10, 2018 at 22:30
  • $\begingroup$ Thank you very much for the reference, it was very useful! $\endgroup$
    – Javier
    Aug 11, 2018 at 16:47
  • $\begingroup$ Can anyone tell me why the Visibility Function is normalized to 1.0? What were the units before it was normalized? I'm trying to do this calculation myself and could use a reference. $\endgroup$
    – user32023
    Aug 30, 2019 at 23:43

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