Recent polarimetric surveys of extragalactic radio sources (ERS) at frequencies u>1GHz are reviewed. By exploiting all the most relevant data on the polarized emission of ERS we study the frequency dependence of polarization properties of ERS betwee
n 1.4 and 86GHz. For flat-spectrum sources the median (mean) fractional polarization increases from 1.5% (2-2.5%) at 1.4GHz to 2.5-3% (3-3.5%) at u>10GHz. Steep-spectrum sources are typically more polarized, especially at high frequencies where Faraday depolarization is less relevant. As a general result, we do not find that the fractional polarization of ERS depends on the total flux density at high radio frequencies, i.e >20GHz. Moreover, in this frequency range, current data suggest a moderate increase of the fractional polarization of ERS with frequency. A formalism to estimate ERS number counts in polarization and the contribution of unresolved polarized ERS to angular power spectra at Cosmic Microwave Background (CMB) frequencies is also developed and discussed. As a first application, we present original predictions for the Planck satellite mission. Our current results show that only a dozen polarized ERS will be detected by the Planck Low Frequency Instrument (LFI), and a few tens by the High Frequency Instrument (HFI). As for CMB power spectra, ERS should not be a strong contaminant to the CMB E-mode polarization at frequencies u>70GHz. On the contrary, they can become a relevant constraint for the detection of the cosmological B--mode polarization if the tensor-to-scalar ratio is <0.01.
We present models to predict high frequency counts of extragalactic radio sources using physically grounded recipes to describe the complex spectral behaviour of blazars, that dominate the mm-wave counts at bright flux densities. We show that simple
power-law spectra are ruled out by high-frequency (nu>100 GHz) data. These data also strongly constrain models featuring the spectral breaks predicted by classical physical models for the synchrotron emission produced in jets of blazars (Blandford & Konigl 1979; Konigl 1981). A model dealing with blazars as a single population is, at best, only marginally consistent with data coming from current surveys at high radio frequencies. Our most successful model assumes different distributions of break frequencies, nu_M, for BL Lacs and Flat-Spectrum Radio Quasars (FSRQs). The former objects have substantially higher values of nu_M, implying that the synchrotron emission comes from more compact regions; therefore, a substantial increase of the BL Lac fraction at high radio frequencies and at bright flux densities is predicted. Remarkably, our best model is able to give a very good fit to all the observed data on number counts and on distributions of spectral indices of extragalactic radio sources at frequencies above 5 and up to 220 GHz. Predictions for the forthcoming sub-mm blazar counts from Planck, at the highest HFI frequencies, and from Herschel surveys are also presented.
