Constraints on $CPT$ violation from Wilkinson Microwave Anisotropy Probe three year polarization data: A wavelet analysis

We perform a wavelet analysis of the temperature and polarization maps of the cosmic microwave background (CMB) delivered by the Wilkinson Microwave Anisotropy Probe experiment in search for a parity-violating signal. Such a signal could be seeded by new physics beyond the standard model, for which the Lorentz and $CPT$ symmetries may not hold. Under these circumstances, the linear polarization direction of a CMB photon may get rotated during its cosmological journey, a phenomenon also called cosmological birefringence. Recently, Feng et al. have analyzed a subset of the Wilkinson Microwave Anisotropy Probe and BOOMERanG 2003 angular power spectra of the CMB, deriving a constraint that mildly favors a nonzero rotation. By using wavelet transforms we set a tighter limit on the CMB photon rotation angle $\Delta \alpha =-2.5\pm 3.0$ ($\Delta \alpha =-2.5\pm 6.0$) at the one (two) $\sigma$ level, consistent with a null detection.

Figure 1

MC means for $X^{TC}$ (see text), for $-8°\le \Delta \alpha \le 8°$, step of 1° (dashed lines refer to positive $\Delta \alpha$, the middle line is for $\Delta \alpha =0$, i.e. $P$ is conserved). The scale $R$ is given in arcminutes. The shaded region shows the $1\sigma$ range for $\Delta \alpha =0$. Experimental points (WMAP3) are shown as crosses.

Figure 2

Same as Fig. 1 but for $X^{GC}$ and $-16°\le \Delta \alpha \le 16°$, step of 2°. Note the lower signal to noise.

Figure 3

Likelihood functions of the cosmological birefringence angle $\Delta \alpha$ for $CG$ (dotted) and $TC$ (dashed), computed from the wavelet estimator on WMAP3 data. The solid (blue) line is the global, covariance weighted, likelihood.

Figure 4

${\chi }^2$ of the cosmological birefringence angle $\Delta \alpha$ in case of pure signal using the wavelets estimator of the component $TC$ (dotted) and the angular power spectrum $C_l^{TC}$ (solid).