Searching for $CPT$ Violation with Cosmic Microwave Background Data from WMAP and BOOMERANG

We search for signatures of Lorentz and $CPT$ violations in the cosmic microwave background (CMB) temperature and polarization anisotropies by using the Wilkinson Microwave Anisotropy Probe (WMAP) and the 2003 flight of BOOMERANG (B03) data. We note that if the Lorentz and $CPT$ symmetries are broken by a Chern-Simons term in the effective Lagrangian, which couples the dual electromagnetic field strength tensor to an external four-vector, the polarization vectors of propagating CMB photons will get rotated. Using the WMAP data alone, one could put an interesting constraint on the size of such a term. Combined with the B03 data, we found that a nonzero rotation angle of the photons is mildly favored: $\Delta \alpha =-6.0\genfrac{}{}{0ex}{}{+4.0}{-4.0}\genfrac{}{}{0ex}{}{+3.9}{-3.7}\mathrm{deg}(1,2\sigma )$.

Figure 1

One-dimensional constraints on the rotation angle $\Delta \alpha$ from WMAP data alone (green or light gray line), WMAP and the 2003 flight of BOOMERANG B03 TT, TG, GG and CC (orange or gray line), and from WMAP and the full B03 observations (TT, TG, GG, CC, TC, GC) (black line).

Figure 2

One-dimensional constraints on the rotation angle $\Delta \alpha$ from WMAP and the B03 observations, assuming only CMB TC is rotated to be nonzero by $\Delta \alpha$ (green or gray line) and only GC rotated (black line).

Figure 3

Joint two-dimensional posterior probability contour plots in the $\Delta \alpha -{\tau }_r$ (top left panel), $\Delta \alpha -n_S$ (top right panel), $\Delta \alpha -\log [{10}^{10}{A}_S]$ (bottom left panel), and $\Delta \alpha -r$ (bottom right panel), showing the 68% and 95% contours from the $\mathrm{WMAP}+\mathrm{B}03$ constraints.