I was reading Wayne Hu's CMB polarisation notes (https://arxiv.org/pdf/astro-ph/9706147.pdf) and at the bottom of page 14 he says;

For $z_{ri}∼5–20$ the difference in the power spectrum is confined to large angles (ℓ <30). Here the observations are limited by “cosmic variance”: the fact that we only have one sample of the sky and hence only 2ℓ+ 1 samples of any given multipole. Cosmic variance is the dominant source of uncertainty on the low-ℓ temperature spectrum in Fig. 14.

The same is not true for the polarization. As we have seen the polarization spectrum is very sensitive to the epoch of last scattering. More specifically, the location of its peak depends on the horizon size at last scattering and its height depends on the duration of last scattering (Efstathiou 1988). This signature is not cosmic variance limited until quite late reionization, though the combination of low optical depth and partial polarization will make it difficult to measure in practice (see Fig. 14 andTable 2).

Is this implying that cosmic variance doesn't affect E and B mode polarisation (as it looks from Planck spectra) and if not why not?


1 Answer 1


Cosmic variance still affects polarization anisotropy measurements. Hu is saying that these measurements are “not cosmic variance limited” until late reionization, meaning that uncertainty in reionization time is the dominant source of error on these scales. In contrast, the TT spectrum is dominated by cosmic variance at large angular scales (the measurement is “limited” by cosmic variance in that the error cannot be reduced with more precise instruments or more data).


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