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Linear Power Spectrum

  1. Dec 13, 2013 #1
    Dear Experts,

    I try to understand power spectra for large scale structure and CMB analyses for my exams.

    I constantly find the expression for linear power spectra [itex]P(k) = A\cdot k^{n_s}\cdot T^2(k)[/itex]. I understand that this comes from primodial primodial fluctuations and the tranfer function kind of "evolves" the spectrum to our time.

    What I don't understand is the following: Why does the BAO make wiggles? I the correlation function there is only one bump from BAO, as much as I know.
    What is the nonlinear power spectrum? Why are the wiggles removed from the plots sometimes in the analyses?

    Thank you
  2. jcsd
  3. Dec 13, 2013 #2


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    Don't be offended if I address this at a very basic level--you may be well advanced beyond what I have to say. For basic physical intuition look at this ball and spring graphic at Wayne Hu's website
    This is a page of his "tour of CMB"
    He calls that page "seeing sound".
    The acoustic peaks of the CMB power arise from sound vibrations in the hot gas that we see at the moment that photons experienced "last scattering" and were decoupled from the gas. CMB is like a photograph of a bunch of ripples made by tossing a handful of pebbles of different sizes into a pool of water.

    I wouldn't spend much time with Wayne Hu's explanation. Just look at a few of his graphics to get some physical intuition. Lineweaver has what I think is a clear and more concise explanation.

    For a start, to understand in more detail, you could look at Lineweaver's Figure 11 on this page.
    also read the paragraph of explanation right under Figure 11.

    This material is ten years old (Lineweaver 2003). There may be better stuff out there now but this is pretty clear and will give you a start if you need an introduction. (Of course you may be well above this level, I can't tell.)

    Figure 11 shows how the basic mechanism depends on patches of dark matter overdensity
    which form potential wells into which ordinary (baryonic) matter can fall and bounce and fall and bounce and…

    The matter and its heat radiation photons are COUPLED by scattering so the photons are trapped in the cloud of partially ionized gas. The photons generate RADIATON PRESSURE within the gas. So gravity pulls it into the well and pressure bounces it out.

    The POWER of the temperature fluctuations we see is the sum of two effects which Figure 11 calls "adiabatic" and "doppler". You can see that the highest peaks come at scales where those two effects ADD.

    For me that is the most interesting thing about Figure 11. I hope we can continue talking about the CMB acoustic oscillations (they eventually influenced the variations in spacing between galaxies!!! and the effect can be measured). Also hopefully other people will contribute to discussion. This is all I have time for now. Thanks for the question, BAO is a very interesting subject.
    Last edited: Dec 13, 2013
  4. Dec 15, 2013 #3
    Dear marcus,
    thank you very much for the nice links, I appreciate.

    Maybe my question was misleading. The mechanism of the CMB fluctuations is nicely explained but I was more interested in perturbation theory.

    What is the definition of the linear power spectrum? Is the BAO bump in the correlation function at ~100 Mpc/h corresponding to the wiggles in the power spectrum? I also read once that this is an effect of shell crossing without more explanation, can you give me a hint to literature where this is explained?

    Thank you for your effort, as you can see, I am kind of puzzled these days.
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