I briefly review the theory and physics of the cosmic microwave background (CMB) and the CMB temperature and polarization anisotropies. I compare the two formalisms: the total angular momentum method and 1+3 covariant and gaugeinvariant approach, which are quiet efficient and widely used ways to calculate CMB anisotropies in an FriedmanRobertsonWalker (FRW) universe. I apply the total angular momentum method to calculate the power spectrum $C^{BB}_l$ "See full text for abstract." which should be zero in the presence of scalar perturbations. However, the Faraday rotation effect which is induced by a primordial magnetic field would generate it. Thus, the Faraday rotation effects allow me to study the characteristics of a primordial magnetic field. I use the 95\% confidence level BB upper limits data from three experiments: QUIET, QUaD and BICEP to constrain to the magnetic field relative density $\Omega_{B\gamma}$ "See full text for abstract." (or the corresponding effective magnetic field $B_\mathrm{eff}$) "See full text for abstract." and inertial scale $k_I$, separately. I find that QUIET data gives the strongest bound.
Date of Award  1 Aug 2012 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Richard Davis (Supervisor) 

Bmode polarization of the CMB from Faraday rotation by a primordial magnetic field
Li, Y. (Author). 1 Aug 2012
Student thesis: Master of Science by Research