Vertical axis of the CMB power spectrum

In summary, the vertical axis in the CMB power spectrum is usually chosen as ##l(l+1)C_l/2\pi## instead of simply ##C_l## for two main reasons. The first reason is that it allows for a better representation of a scale-invariant Gaussian random field, and the second reason is due to the spherical nature of the harmonics. References from experts in the field support this choice.
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DoobleD
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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## ?

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

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DoobleD said:
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.
 
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DoobleD said:
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.
 
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Awesome, thanks for thoses answers, especially for the references.
 

FAQ: Vertical axis of the CMB power spectrum

1. What is the CMB power spectrum?

The CMB (Cosmic Microwave Background) power spectrum is a graph that shows the distribution of energy in the CMB radiation at different angular scales. It is a crucial tool for studying the structure and evolution of the universe.

2. What is the significance of the vertical axis in the CMB power spectrum?

The vertical axis of the CMB power spectrum represents the amount of energy present at different angular scales. This can tell us about the density and distribution of matter in the universe, as well as the properties of the early universe.

3. How is the vertical axis of the CMB power spectrum determined?

The vertical axis of the CMB power spectrum is determined through measurements of the CMB radiation using specialized instruments like the Planck satellite. The data is then analyzed and plotted on the power spectrum, with the vertical axis representing the level of energy at each angular scale.

4. What do the peaks and dips on the vertical axis of the CMB power spectrum represent?

The peaks and dips on the vertical axis of the CMB power spectrum correspond to different features in the CMB radiation. The first peak represents the largest structures in the universe, while subsequent peaks represent smaller structures. The dips, or valleys, represent regions with lower energy levels.

5. How does the vertical axis of the CMB power spectrum support the Big Bang theory?

The vertical axis of the CMB power spectrum provides strong evidence for the Big Bang theory. The distribution of energy on the vertical axis matches the predicted pattern from the Big Bang model, providing confirmation of the theory's predictions about the early universe.

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