### [1003.0299] The local B-polarization of the CMB: a very sen

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**March 05 2010**Topological defects can source scalar, vector and tensor modes in the early universe. The vector modes have power on small scales and can generate E and B polarization; the B signal can be quite distinctive, and used to constrain defect models with future data.

This paper appears to take some previous results for the B-mode power spectrum and multiply them by l^4, so e.g. in Fig 1 the power is very blue. Of course to be consistent you also have to multiply the noise and the any other spectrum of interest by l^4 as well, so you seem to gain nothing by doing this. Is there some point I have missed?

The paper also defines a 'local' scalar [tex]\tilde{B}[/tex] by taking two derivatives of the polarization tensor. However you gain nothing by doing this; with noisy or non-band-limited data you cannot calculate derivatives on a scale L without having data available over a scale L - the non-locality just hits you in a different form (see astro-ph/0305545 and refs).

This paper appears to take some previous results for the B-mode power spectrum and multiply them by l^4, so e.g. in Fig 1 the power is very blue. Of course to be consistent you also have to multiply the noise and the any other spectrum of interest by l^4 as well, so you seem to gain nothing by doing this. Is there some point I have missed?

The paper also defines a 'local' scalar [tex]\tilde{B}[/tex] by taking two derivatives of the polarization tensor. However you gain nothing by doing this; with noisy or non-band-limited data you cannot calculate derivatives on a scale L without having data available over a scale L - the non-locality just hits you in a different form (see astro-ph/0305545 and refs).