http://arxiv.org/abs/1401.7936
Primordial statistical anisotropy is a key indicator to investigate early Universe models and has been probed by the cosmic microwave background (CMB) anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated from anisotropic gravitational waves, parametrised by $P_h({\bf k}) = P_h^{(0)}(k) [ 1 + \sum_{LM} f_L(k) g_{LM} Y_{LM} (\hat{\bf k}) ]$, where $P_h^{(0)}(k)$ is the usual scale-invariant power spectrum. Such anisotropic tensor fluctuations may arise from an inflationary model with noncommutativity of fields. It is verified that in this model, an isotropic component and a quadrupole asymmetry with $f_0(k) = f_2(k) \propto k^{-2}$ are created and hence highly red-tilted off-diagonal components arise in the CMB power spectra, namely $\ell_2 = \ell_1 \pm 2$ in $TT$, $TE$, $EE$ and $BB$, and $\ell_2 = \ell_1 \pm 1$ in $TB$ and $EB$. We find that B-mode polarisation is more sensitive to such signals than temperature and E-mode polarisation due to the smallness of large-scale cosmic variance and we can potentially measure $g_{00} = 30$ and $g_{2M} = 58$ at 68% CL in a cosmic-variance-limited experiment. These values correspond to the noncommutative parameter of about the size of the present horizon. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the ${\it Planck}$ experiment.
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