Frequency-dependent constraints on cosmic birefringence from the LFI and HFI <i>Planck</i> Data Release 4

We present new constraints on the frequency dependence of cosmic birefringence angle from Planck data release 4 polarization maps. An axion field coupled to electromagnetism predicts a nearly frequency-independent angle, $\beta_\nu = \beta$, while Faraday rotation local magnetic fields and Lorentz violating theories predict that is proportional frequency, $\nu$, power some integer $n$, \propto \nu^n$. In this work, we first sample $\beta_\nu$ individually for each polarized HFI band in addition 70 GHz channel LFI. also constrain power-law formula $\beta_\nu=\beta_0(\nu/\nu_0)^n$, with $\nu_0 150$ GHz. For full-sky measurement, $f_{\text{sky}}=0.93$, find $\beta_0 0.26^{\circ}\pm0.11^\circ$ $(68\% \text{ C.L.})$ $n=-0.45^{+0.61}_{-0.82}$ when ignore intrinsic $EB$ correlations foreground emission, 0.33^\circ \pm 0.12^\circ$ $n=-0.37^{+0.49}_{-0.64}$ use filamentary dust model $EB$. Next, all maps, including 30 44 bands. These bands have negligible contribution emission. We, therefore, treat them separately. Without any modeling foreground, generally inclusion raises measured values tightens $n$. At full-sky, measure $\beta_0=0.29^{\circ+0.10^\circ}_{\phantom{\circ}-0.11^\circ}$ $n=-0.35^{+0.48}_{-0.47}$. Assuming no dependence, $\beta=0.33^\circ 0.10^\circ$. If our measurements effectively mitigated are consistent mostly signal birefringence.