CMB statistical anisotropy from noncommutative gravitational waves

Abstract

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 $P_h(\mathbf{k})=P_h^{(0)}(k)[1+{\sum }_{LM}{f}_L(k)g_{LM}{Y}_{LM}(\hat{\mathbf{k}})]$, 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. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the $Planck$ experiment. These results imply that it is impossible to measure the noncommutative parameter if it is small enough for the perturbative treatment to be valid. Our formalism and methodology for dealing with the CMB tensor statistical anisotropy are general and straightforwardly applicable to other early Universe models.

13 pages, 2 figures, 1 table. Accepted for publication in JCAP

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• Parity-violating and anisotropic correlations in pseudoscalar inflation
• Constraint on noncommutative spacetime from PLANCK data
• Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
• Hunting for Statistical Anisotropy in Tensor Modes with B-mode Observations
• Imprints of the post recombination dissipation of helical magnetic field on the Cosmic Microwave Background Radiation
• Extremal noncommutative black holes as dark matter furnaces