Signatures of anisotropic sources in the squeezed-limit bispectrum of the cosmic microwave background

The bispectrum of primordial curvature perturbations in the squeezed configuration, in which one wavenumber, k sub(3), is much smaller than the other two, k sub(3)[Lt] k sub(1)[Lt] k sub(2), plays a special role in constraining the physics of inflation. In this paper we study a new phenomenological signature in the squeezed-limit bispectrum: namely, the amplitude of the squeezed-limit bispectrum depends on an angle between k sub(1) and k sub(3) such that B sub([zeta])(k sub(1), k sub(2), k sub(3)) [arrowright] 2 [Sigma] sub(L) sub(cL)P sub(L) (k sub(1) [middot] k sub(3))P sub([zeta])(k sub(1))P sub([zeta])(k sub(3)), where P sub(L) are the Legendre polynomials. While c sub(0) is related to the usual local-form f sub(NL) parameter as c sub(0) = 6f sub(NL)/5, the higher-multipole coefficients, c sub(1), c sub(2), etc., have not been constrained by the data. Primordial curvature perturbations sourced by large-scale magnetic fields generate non-vanishing c sub(0), c sub(1), and c sub(2). Inflation models whose action contains a term like I ([phi]) super(2)F super(2) generate c sub(2) = c sub(0)/2. A recently proposed "solid inflation" model generates c sub(2) >> c sub(0). A cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to l sub(max) = 2000 is able to measure these coefficients down to [delta]c sub(0) = 4.4, [delta]c sub(1) = 61, and [delta]c sub(0) = 13 (68% CL). We also find that c sub(0) and c sub(1), and c sub(0) and c sub(2), are nearly uncorrelated. Measurements of these coefficients will open up a new window into the physics of inflation such as the existence of vector fields during inflation or non-trivial symmetry structure of inflaton fields. Finally, we show that the original form of the Suyama-Yamaguchi inequality does not apply to the case involving higher-spin fields, but a generalized form does.