Recently Background Imaging of Cosmic Extragalactic Polarization （B2） discovered the relic gravitational waves at 7.00- confi- dence level. However, the other cosmic microwave background （CMB） data, for example Planck data released in 2013 （P13）, prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter ACDM cosmology. In this paper, we explore whether the wCDM model and the running spectral index can relax the tension between B2 and other CMB data. Specifically we found that a positive running of running of spectral index is preferred at 1.70- level from the combination of B2, P 13 and WMAP Polarization data.
Pulsar timing array(PTA) provides an excellent opportunity to detect the gravitational waves(GWs) in nanoHertz frequency band.In particular, due to the larger number of "arms" in PTA, it can be used to test gravity by probing the non-Einsteinian polarization modes of GWs, including two spin-1 shear modes labeled by "sn" and "se", the spin-0 transverse mode labeled by "b" and the longitudinal mode labeled by "l". In this paper, we investigate the capabilities of the current and potential future PTAs, which are quantified by the constraints on the amplitudes parameters(c_b, c_(sn), c_(se), c_l), by observing an individual supermassive black hole binary in Virgo cluster. We find that for binary with total mass M_c= 8.77 × 10~8 M_⊙ and GW frequency f = 10^(-9) Hz, the PTA at current level can detect these GW modes if c_b> 0.00106, c_l> 0.00217, c_(se)> 0.00271, c_(sn)> 0.00141, which will be improved by about two orders if considering the potential PTA in SKA era. Interesting enough, due to effects of the geometrical factors, we find that in SKA era, the constraints on the l, sn, se modes of GWs are purely dominated by several pulsars, instead of the full pulsars in PTA.
The anisotropies of the B-mode polarization in the cosmic microwave background radiation play a crucial role in the study of the very early Universe. However, in real observations, a mixture of the E- mode and B-mode can be caused by partial sky surveys, which must be separated before being applied to a cosmological explanation. The separation method developed by Smith （2006） has been widely adopted, where the edge of the top-hat mask should be smoothed to avoid numerical errors. In this paper, we compare three different smoothing methods and investigate leakage residuals of the E-B mixture. We find that, if less information loss is needed and a smaller region is smoothed in the analysis, the sin- and cos-smoothing methods are better. However, if we need a cleanly constructed B-mode map, the larger region around the mask edge should be smoothed. In this case, the Gaussian-smoothing method becomes much better. In addition, we find that the leakage caused by numerical errors in the Gaussian-smoothing method is mostly concentrated in two bands, which is quite easy to reduce for further E-B separations.
