Analysis of Cosmic Microwave Background Polarisation

  • Michael Preece

Student thesis: Phd


Observations of the Cosmic Microwave Background (CMB) radiation are an extremely important tool for understanding the Universe. The next generation of CMB experiments will attempt to measure the polarisation signal. In particular, the detection of B-mode polarisation, which is mainly generated by gravitational waves from the very early Universe, would provide a strong indicator for the energy level of inflation. However, due to the relative weakness of this signal, and the fact that there exists a much stronger E-mode signal, detecting B-modes polarisation poses several technical challenges. In particular, the standard method of CMB analysis, the pseudo-C_l method, is insufficient for the purposes of analysing B-mode polarisation, because of the difficulties of separating E and B mode polarisation on a cut sky. However, an alternate method, the pure-C_l method, has recently been outlined, which removes the effect of E-B mixing by subtracting out ambiguous modes.In order to test this method, I have written code to implement my own version of the algorithm, as well as the ordinary pseudo-C_l method. I have then used this code to compare the two methods both with and without E-modes, thereby demonstrating that the pure-C_l method does not suffer from issues with E-B mixing. However, I also find that, due to the effects of subtracting out ambiguous modes, the performance of the pure-C_l method is degraded on large scales, by a factor which is dependent on the length of the mask boundary. I have, therefore, investigated this effect. I find that, in general, the issues with this method are limited to only the very largest scales, and they are unlikely to cause significant problems for most masks. However, due to the nature of point source masks, these are particularly susceptible to such effects. Therefore, I have considered this case more carefully. Here, I find that there is indeed a significant effect up to multipoles of l ~ 50, and I have discovered that there is a simple relationship between the additional error caused by a point source mask and the number of sources. Due to the rapidly rising (in l^2 C_l) nature of the point-source power-spectrum, this issue can probably be avoided by only using the point-source mask for high-l measurements and, thus, the effect of point sources on the pure-C_l method will probably be limited. The exception to this, however, is the case where an exceptionally large number of sources must be masked out. In this case, the requirement to apodise the mask in order to implement the method will result in the analysis breaking down.Additionally, I have also looked at several other aspects of B-mode detection. I used various optimal error formulae, in conjunction with my pure-C_l code, to attempt to determine the optimal scan strategy for a given set of parameters, with a particular focus on the QUIJOTE experiment. Ultimately, it was found that this experiment in its original form would only be able to detect values of r of around 0.2, although increasing the number of beams would improve this slightly. Finally, I have outlined a novel null test that is designed to detect systematic errors in CMB experiments using polarisation position angles. I have showed that this method will be able to detect shear-like systematic errors at a level of less than 1%.
Date of Award31 Dec 2011
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorRichard Battye (Supervisor)

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