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FERMILAB-Pub-96/068-A Comment on a Paper by Fang, Huang, and

By Scott Dodelson and Albert Stebbins


Before decoupling in the early universe, the tightly coupled photon/electron gas underwent acoustic oscillations. These oscillations should be visible today in the spectrum of anisotropies. Recently Fang, Huang, and Wu (1996) claimed that when random processes are accounted for, the phases of these oscillations are no longer coherent. In fact, they claim that the well-defined peaks will be completely smoothed out. We show here that their claim is incorrect. The standard Boltzmann treatment determining the anisotropies is sufficient; random processes do not change the standard result. Our criticism has two parts, both dealing with their equation 26. The first point is that – at least to a first approximation – the power spectrum today is caused by the monopole at decoupling. If Θ0 were zero at decoupling there would [again to first approximation] be no anisotropy today. Fang et al. derive an expression for the phase shift for each of the l − modes (their eqn. 25), but the only one of these phase shifts that is relevant is the l = 0 mode. All the higher modes [with the minor exception of the l = 1 mode] 1 have negligible amplitudes in the tightly coupled regime. The final anisotropy spectrum today depends then only on this one phase shift δφ0(η∗). So we disagree with eqn 26 which assumes that the shift in a given multipole of the power spectrum depends on the phase shift of that multipole at decoupling. To make this slightly more quantitative, let us write the standard expression for the power spectrum

Year: 1996
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