• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,734 comments
1,470 users with positive rep
818 active unimported users
More ...

  Why is the CMB (nearly) scale invariant?

+ 6 like - 0 dislike

Why is the power spectrum of the cosmic microwave background nearly scale-invariant? What are the mechanisms that make it deviate from the scale-invariance. And in fact: why is it scale invariant in the first place?

Does the motivation come from experiment, which is then tried to be achieved in a specific model, or directly from the model?

This post imported from StackExchange Physics at 2014-06-21 21:38 (UCT), posted by SE-user Anne O'Nyme
asked Jun 20, 2014 in Theoretical Physics by Anne O'Nyme (175 points) [ no revision ]
What makes you think it is scale invariant? The power in fluctuations on different scales varies by a factors of a few. Are you asking why it is nearly isotropic (variations on only one part in $\sim10^5$ in different directions on the sky)?

This post imported from StackExchange Physics at 2014-06-21 21:38 (UCT), posted by SE-user Kyle
@Kyle Then my question is as follows: were the fluctuations scale invariant from the beginning (by this I mean before decoupling) and is the damping and enhancement features of the power spectrum due to Silk damping and baryonic loading which came later. Or were some fluctuation fluctuations already `preferred' wrt to others before decoupling?

This post imported from StackExchange Physics at 2014-06-21 21:38 (UCT), posted by SE-user Anne O'Nyme

1 Answer

+ 1 like - 0 dislike

These are just some rather handwaving comments related to why the spectrum of the fluctuations in the CMB are of expected to be scale invariant.

The variations of the CMB we observe today correspond to the expanded initial over-dense and under-dense regions created by vacuum fluctuations.

The theoretical expectation of scale invariance of the spectrum of these fluxtuations can for example be explained by looking at a scalar field with the Lagrangian density

\(L = \frac{1}{2}\dot{\phi^2} + \frac{1}{2} (\nabla\phi)^2 - V(\phi)\)

Multiplying by the volume of space $a^3(t)$, assuming that any spatial gradients are stretched out by inflation, and making use of the Euler-Lagrange equations it can be shown that the equation of motion corresponds to damped harmonic oscillator

\(\ddot{\phi} + 3 H \dot{\phi } = -\frac{\partial V}{\partial \phi}\)

where the second term in the L.H.S. is the so-called Hubble friction. Together with the quantum fluctuations, a scale invariant CMB spectrum can then theoretically be expected, as quantum fluctuations are excited at small scales, subsequently enlarged by the expansion of the universe, and finally dissipated (frozen out) by the Hubble friction at large scales as soon as their wave length gets larger than the light horizon (separation over which information can be exchanged). 

I am not sure what processes there could be that lead to deviations of the CMB spectrum from scale invariance.

answered Jun 28, 2014 by Dilaton (6,240 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights