Features:

1. The graph is rather difficult to interpret simply at the intro astro level. For a rather full explication of what it means well beyond the intro astro level, see Review of the Universe: Power Spectrum.

2. However, if you have ever played around with at musical synthesizer (NOT yours truly), then you know that you can superimpose sound oscillations of different frequencies to create a complex series of of sound oscillations in the time domain.

   The strength or weight of each specified frequency can be called its power (which is defined variously) and you can graph power versus frequency to analyze your wonderful musical creation, harmonious or discordant.

   The CMB:

   1. Replace time domain by the celestial sphere (i.e., the 4π solid angle of the all the sky).
   2. Replace frequencies by spherical harmonics: a set of oscillations of some variable on the surface of a sphere. For the CMB, the variable is temperature Note, frequency forms a continuum, but the spherical harmonics form a discrete, but infinite, set. However, the set of spherical harmonics is a complete orthonormal basis??? which any sufficiently smooth function??? a can be written as a linear combination of spherical harmonics: i.e., can be expanded into series of weighted spherical harmonics that is usually infinite.
   3. For your musical composition you choose the weights or powers. For the CMB, Big Bang (at lookback time = age of the observable universe = 13.797(23) Gyr (Planck 2018) including inflation (during the inflation era (cosmic time ∼ 10**(-36)--10**(-33) or 10**(-32) s from fiducial time zero of standard Friedmann equation models)) chose the powers (an infinite set of them) for the spherical harmonics and we must deduce these powers from the CMB by multipole analysis. Why are the coefficients of the cmb power spectrum multiplied by l(l+1)?. cosmic microwave background (CMB) temperature fluctuations

3. But rather vaguely??? weight of .... ??? (as indicated by the upper axis) on the sky in the cosmic microwave background (CMB) (CMB mean temperature T = 2.72548(57) K (Fixsen 2009) (FK-652--653). The large/small angular separations are on the left/right.

   The data points come from various experiments of the : WMAP (2001--2010), ACBAR (2000-2008), BOOMERanG (1997--2003), CBI (1999--2008), and VSA (2000---2008).

4. The actual all-sky sky map (4π of solid angle sky map as seen from the Earth) of the cosmic microwave background (CMB, T = 2.72548(57) K (Fixsen 2009)) show an average temperature (i.e., CMB T = 2.72548(57) K (Fixsen 2009)) on which are superimposed small variations of order 1/25000 ???? on many angular scales (e.g., 90°, 2°, 0.2° as illustrated on the graph, but requiring some explication).

   The "topography" of the fluctuations can be decomposed into an expansion in spherical harmonics (i.e., the CMB multipole analysis):

    T(θ,φ)=∑_(ℓ,m) a_(ℓ,m)Y_{ℓ,m)(θ,φ)  , 

   where the Y_{ℓ,m)(θ,φ) are the spherical harmonics and the a_(ℓ,m) their weights in the expansion.

   For ????

     C_(ℓ)=sum_(m) |a_(ℓ,m)|**2/[ℓ(ℓ+1)] 

   For ??? plotting

     [ℓ(ℓ+1)]C_(ℓ)/(2π) 

   The points of C_(ℓ) are connnected by by a curve to create pseudo continuum of points of C_(ℓ). The multiplication by [ℓ(ℓ+1)] is graphing convention to compress the vertical scale. The power at the highest peak at ℓ=200 is really 6000/(200**2) = 2.4 which moderately small compared to the power at ℓ=10 which is 800/(10**2) = 8.

   The associated Legendre polynomials Legendre polynomials Legendre polynomial zeros (ℓ in (0,&pi:) or 2ℓ ∈(0,2&;pi;)), and so the averge size of an up or down fluctuation is $2&pi/(2ℓ)=180°/ℓ (e.g., 180°/90 = 2°)

The fact that the inflation paradigm predicted the observations is an astonishing triumph of the inflation paradigm.

The successful prediction does NOT prove the inflation paradigm, but it certainly strongly supports it.

Credit/Permission: NASA, WMAP Science Team, 2006 (uploaded to Wikimedia Commons by User:Pieter_Kuiper, 2007) / Public domain.
Image link: Wikimedia Commons: File:PowerSpectrumExt.svg.
Local file: local link: cmb_power_spectrum.html.
File: Cosmology file: cmb_power_spectrum.html.