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I Getting the wrong multipole for 1st acoustic peak

  1. Aug 19, 2017 #1
    I'm trying to do a simple calculation, but there must be something wrong.

    The wavelength ##\lambda_1## corresponding to first acoustic peak of the CMB is related to the sound horizon at last scattering, ##d_{hs}##, by :

    ## \lambda_1 = 2d_{hs} ## (see for instance slide 14 on Wayne Hu PDF slides).

    Now, the multipole ##l## of the first acoustic peak can be related to its wavelength and to the distance to last scattering surface, ##D##, by :

    ##l_1 = \frac{2 \pi}{\lambda_1} D## (see slide 15)

    From that I deduce the following equation :

    ##l_1 = \frac{\pi}{d_{hs}}D##

    I find in the litterature that ##D \approx 14000 Mpc##, and ##d_{hs} \approx 150 Mpc##. I plug those values into the previous equation, and I find ##l_1 \approx 293##, which is quite far from the ##l_1 \approx 200## I should get for the first peak. What's wrong ?
     
  2. jcsd
  3. Aug 19, 2017 #2
    I get the values for distance to last scattering surface and sound horizon here. I wonder however if 150 Mpc for the sound horizon is not in comoving coordinates, while I should use the physical distance instead (which I don't know) ?

    EDIT : I just realized that at the very end of that WMAP values document, they basically give the exact same formula, ##l = \frac{\pi}{d_{hs}}D##. And with the values they gives, I get ##l = 299##. Why am I not getting 200 ?
     
    Last edited: Aug 19, 2017
  4. Aug 19, 2017 #3
  5. Aug 21, 2017 #4

    bapowell

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  6. Sep 5, 2017 #5
    Thank you for the help. I'm still puzzled by my problem, but great article.
     
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