Revealing cosmic rotation

Cosmological Birefringence, a rotation of the polarization plane of radiation coming to us from distant astrophysical sources, may reveal parity violation in either the electromagnetic or gravitational sectors of the fundamental interactions in nature. Until only recently this phenomenon could be probed with only radio observations or observations at UV wavelengths. Recently, there is a substantial effort to constrain such nonstandard models using observations of the rotation of the polarization plane of cosmic microwave background (CMB) radiation. This can be done via measurements of the $B$-modes of the CMB or by measuring its $TB$ and EB correlations which vanish in the standard model. In this paper we show that $EB$ correlations-based estimator is the best for upcoming polarization experiments. The $EB$-based estimator surpasses other estimators because it has the smallest noise and of all the estimators is least affected by systematics. Current polarimeters are optimized for the detection of $B$-mode polarization from either primordial gravitational waves or by large-scale structures via gravitational lensing. In the paper we also study the optimization of CMB experiments for the detection of cosmological birefringence, in the presence of instrumental systematics, which by themselves are capable of producing $EB$ correlations, potentially mimicking cosmological birefringence.

Figure 1

Detectability of CB using the $EB$ estimator. We show the $EB$ estimator noise, $N(L)$, as given by Eq. (9), as a function of multipole $L$. We show the noise for four experimental setups. The noise, ${\Delta }_T$ in $\mu \mathrm{K}-\mathrm{arcmin}$ and beam full-width at half-maximum ${\Theta }_{\mathrm{FWHM}}$–units of arcmin, is labeled. For reference, the two solid curves (black) show the Faraday rotation power spectrum from the stochastic magnetic field with “causal spectrum” ($2n=5.0$) and for a nearly scale-invariant spectrum ($2n=0.1$).

Figure 2

Comparison of the $EB$ and $TB$ estimator for constant $\alpha$ case. We show forecasted uncertainties on constant $\alpha$ from the two estimators as a function of sky-fraction $f_{\mathrm{sky}}$, for several choices of instrumental noise. The dashed-dotted curves (red) are for the $EB$ estimator while the solid curves (black) are for the $TB$ estimator. Clearly the $EB$ estimator outperforms the $TB$ estimator for the experiments with low enough noise such as EBEX [40], CMBPol [26], POLARBEAR [31], SPTPol [41], and SPIDER [42]. Note that for a given observing time, the noise ${\Delta }_T$ is proportional to $\sqrt{f_{\mathrm{sky}}}$ and hence can be reduced by observing smaller sky-fractions.

Figure 3

Forecasted uncertainties on constant $\alpha$ from the $EB$ estimator as a function of sky-fraction $f_{\mathrm{sky}}$, for several choices of instrumental noise. The minima for the curves are a result of compromise between number of modes and noise ${\Delta }_p$. Note that the observing time was fixed.