Why is the CMB power spectrum often plotted as l(l+1) C_l and not only C_L ?

In summary, the conversation discusses the reason for plotting the CMB power spectrum in the specific way shown in the provided image. The y-axis is represented as $$C_\ell \ell (\ell+1)$$ instead of just $$C_\ell$$ because it approximates the power per unit logarithmic interval in \ell. This results in a flat line on a log scale, which is expected for large angular scales (low \ell), explaining the appearance of a plateau in the graph.
  • #1
Anne-Sylvie
12
0
Hello everybody, (sorry for the eventual Engrish)

I can't find any convincing answer for the following question :

Why do we always (or often) plot the CMB power spectrum in this way :
jb.man.ac.uk/research/cosmos/vsa/images/CMB_power_spectrum.gif

I mean the y-axis is $$C_\ell \ell (\ell+1)$$ and not only $$C_\ell. $$ Why ?

Thanks for your answer. I already heard that its because of we want show the plateau at low l. But if it is the answer, why is the plateau proportional to $$\ell (\ell +1) ?$$

Thanks :)
 
Space news on Phys.org
  • #2
From http://relativity.livingreviews.org/open?pubNo=lrr-1998-11&page=articlesu14.html
The reason for plotting [itex]\ell \left( \ell + 1 \right) C_\ell[/itex] is that it approximately equals the power per unit logarithmic interval in [itex]\ell[/itex].

If a log scale is used for [itex]\ell[/itex], scale invariance is a flat line. Scale invariance is expected at large angular scales (low [itex]\ell[/itex]), hence the plateau.
 
Last edited by a moderator:

1. Why is the CMB power spectrum often plotted as l(l+1) C_l?

The CMB power spectrum is often plotted as l(l+1) C_l because it helps to highlight the characteristic shape of the spectrum. This formula, known as the "angular power spectrum," takes into account the dependence of the CMB power on the angular scale l, and helps to separate out the different contributions to the overall power spectrum.

2. What is the significance of the l(l+1) term in the CMB power spectrum formula?

The l(l+1) term in the CMB power spectrum formula is a result of the spherical harmonics used to describe the CMB anisotropies. This term helps to account for the fact that the power spectrum varies with the angular scale l, and is necessary for accurately describing the shape of the spectrum.

3. Why is the CMB power spectrum plotted as a function of l?

The CMB power spectrum is plotted as a function of l because the CMB anisotropies are most efficiently described in terms of multipole moments, which are related to the angular scale l. By plotting the power spectrum as a function of l, we can more easily compare the different contributions to the overall anisotropy.

4. What is the advantage of using l(l+1) C_l instead of just C_l for plotting the CMB power spectrum?

The advantage of using l(l+1) C_l instead of just C_l is that it helps to separate out the different contributions to the overall power spectrum. This makes it easier to analyze and interpret the data, and also helps to highlight the characteristic shape of the spectrum.

5. Can the CMB power spectrum be plotted using a different formula?

Yes, the CMB power spectrum can be plotted using different formulas, such as the C_l formula. However, the l(l+1) C_l formula is the most commonly used because it is better suited for describing the characteristic shape of the spectrum and separating out the different contributions to the overall power. Additionally, the l(l+1) C_l formula is better for comparing results from different experiments and for making predictions based on theoretical models.

Similar threads

A Angular power spectrum dependence in redshift z and k
    • Cosmology
Replies
5
Views
1K
I Vertical axis of the CMB power spectrum
    • Cosmology
Replies
3
Views
2K
A Relation between Matter Power spectrum and Angular power spectrum
    • Cosmology
Replies
2
Views
1K
A Calculate variance on the ratio of 2 angular power spectra
    • Cosmology
Replies
1
Views
753
A Analytical expression of Cosmic Variance - Poisson distribution?
    • Cosmology
Replies
1
Views
771
A Angular power spectrum, bias from N weighted events
    • Cosmology
Replies
2
Views
1K
Understanding the Linear Power Spectrum: How Do BAOs Create Wiggles?
    • Cosmology
Replies
2
Views
3K
I General questions about the CMB
    • Cosmology
Replies
7
Views
1K
A Force to fix sigma8 or A_s for Forecasts
    • Cosmology
Replies
1
Views
1K
I Some questions about Cosmic Microwave Background radiation
    • Cosmology
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top