The TT, TB, EB and BB correlations in anisotropic inflation

The ongoing and future experiments will measure the B-mode from different sky coverage and frequency bands, with the potential to reveal non-trivial features in polarization map. In this work we study the TT, TB, EB and BB correlations associated with the B-mode polarization of CMB map in models of charged anisotropic inflation. The model contains a chaotic-type large field complex inflaton which is charged under the $U(1)$ gauge field. We calculate the statistical anisotropies generated in the power spectra of the curvature perturbation, the tensor perturbation and their cross-correlation. It is shown that the asymmetry in tensor power spectrum is a very sensitive probe of the gauge coupling. While the level of statistical anisotropy in temperature power spectrum can be small and satisfy the observational bounds, the interactions from the gauge coupling can induce large directional dependence in tensor modes. This will leave interesting anisotropic fingerprints in various correlations involving the B-mode polarization such as the TB cross-correlation which may be detected in upcoming Planck polarization data. In addition, the TT correlation receives an anisotropic contribution from the tensor sector which naturally decays after $l \gtrsim 100$. We expect that the mechanism of using tensor sector to induce asymmetry at low $l$ to be generic which can also be applied to address other low $l$ CMB anomalies.Comment: 27 pages, 10 figures; v2: references added; minor improvements in discussion; v3: version published on JCA

Statistical Anisotropies in Gravitational Waves in Solid Inflation

Solid inflation can support a long period of anisotropic inflation. We calculate the statistical anisotropies in the scalar and tensor power spectra and their cross-correlation in anisotropic solid inflation. The tensor-scalar cross-correlation can either be positive or negative, which impacts the statistical anisotropies of the TT and TB spectra in CMB map more significantly compared with the tensor self-correlation. The tensor power spectrum contains potentially comparable contributions from quadrupole and octopole angular patterns, which is different from the power spectra of scalar, the cross-correlation or the scalar bispectrum, where the quadrupole type statistical anisotropy dominates over octopole.Comment: 30 pages, 11 figure