We discuss the effect of matter reionization on the large-angular-scale anisotropy and polarization of the cosmic microwave background radiation (CMBR) in the standard CDM model. We separate three cases in which the anisotropy is induced by pure scalar, pure tensor, and mixed metric perturbations respectively. It is found that, if reionization occurs early enough, the polarization can reach a detectable level of sequentially 6%, 9%, and 6.5% of the anisotropy. In general, a higher degree of polarization implies a dominant contribution from the tensor mode or reionization at high redshift. Since early reionization will suppress small-scale CMBR anisotropies and polarizations significantly, measuring the polarization on few degree scales can be a direct probe of the reionization history of the early universe.

The anisotropy and polarization of the cosmic microwave background radiation (CMBR) induced by the scalar and tensor metric perturbations are computed in the long-wavelength limit. It is found that the large-scale polarization of CMBR induced by the decaying tensor mode can reach a few percents. This is different from the scalar or inflation-induced tensor mode, whereas the polarization is at least two orders of magnitude lower. The effect of matter re-ionization on CMBR is also considered.We conclude that measuring the polarization of CMBR on large-angular scales can probe the ionization history of the early Universe, and test different cosmological models.

Grounded in self-determination theory, the purpose of this study was to investigate the relationships between autonomy-supportive teaching, mindfulness, and basic psychological need satisfaction/frustration. Secondary school students (n = 390, Mage = 15) responded to a survey form measuring psychological constructs pertaining to the research purpose. A series of multiple regression analysis showed that autonomy-supportive teaching and mindfulness positively predicted need satisfaction and negatively predicted need frustration. In addition, the associations between autonomy-supportive teaching and need satisfaction/frustration were moderated by mindfulness. Students higher in mindfulness were more likely to feel need satisfaction and less likely to experience need frustration, even in a low autonomy-supportive teaching environment. These results speak to the relevance of creating autonomy-supportive teaching environments and highlight mindfulness as a potential pathway to basic psychological need satisfaction in educational settings.

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