In Dodelson's "Modern Cosmology" on p.241 he states that the ##a_{lm}##-s -- for a given ##l##-- corresponding to a spherical harmonic expansion of the photon-temperature fluctuations, are drawn from the same probability distribution regardless of the value of ##m##. Dodelson does not explain this any further, but other authors claim that it is due to the fact that ##m## somehow corresponds to an orientation and this should not matter as the universe is (believed to be) statistically rotational invariant.(adsbygoogle = window.adsbygoogle || []).push({});

Question:

What is the precise property of the spherical harmonic ##Y_l^m## for a given ##l## that justifies this claim?

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# CMB , Spherical Harmonics and Rotational Invariance

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