Vertical axis of the CMB power spectrum

[DoobleD]

Why is the vertical axis in the CMB power spectrum usually chosen as $l(l+1)C_l/2\pi$ instead of simply $C_l$ ?

The only answer I found come from this post on stackexchange, but the answer doesn't seem very complete. Anyone knows ?

 

[George Jones]

Why is the vertical axis in the CMB power spectrum usually chosen as $l(l+1)C_l/2\pi$ instead of simply $C_l$ ?

The only answer I found come from this post on stackexchange, but the answer doesn't seem very complete. Anyone knows ?

Rennie's first reason often is given as the reason, e.g., page 243 from the book "Modern Cosmology" by Scott Dodelson, and section 4.1 from the article "COSMIC BACKGROUND RADIATION MINI-REVIEW" by Scott and Smoot,

https://arxiv.org/abs/astro-ph/0406567

Rennie's second reason also is plausible.

 

[kimbyd]

Why is the vertical axis in the CMB power spectrum usually chosen as $l(l+1)C_l/2\pi$ instead of simply $C_l$ ?

View attachment 224824

The only answer I found come from this post on stackexchange, but the answer doesn't seem very complete. Anyone knows ?

If the CMB power spectrum were simply a scale-invariant Gaussian random field, then its power spectrum plotted with that vertical axis would be essentially flat (up to variation due to cosmic variance/instrumental noise). I believe the factor $\ell(\ell+1)$ stems from the fact that the spherical harmonics are not strictly flat plane waves.

 

[DoobleD]

Awesome, thanks for thoses answers, especially for the references.