## Abstract

Soft limits of N-point correlation functions, in which one wavenumber is much smaller than the others, play a special role in constraining the physics of inflation. Anisotropic sources such as a vector field during inflation generate distinct angular dependence in all these correlators, and introduce a fix privileged direction in our sky. In this paper we focus on the four-point correlator (the trispectrum T). We adopt a parametrization motivated by models in which the inflaton φ is coupled to a vector field through a I ^{2}(φ)F^{2} interaction, namely T_{ζ}(k _{1},k_{2},k_{3},k_{4})≡∑ _{ndn} [P_{n} (_{1c}̇_{3})+P _{n} (_{1c}̇_{12})+P_{n} ( _{3c}̇_{12})]P_{ζ} (k_{1})P _{ζ} (k_{3})P_{ζ} (k_{12})+(23perm), where P_{n} denotes the Legendre polynomials. This shape is enhanced when the wavenumbers of the diagonals of the quadrilateral are much smaller than the sides, k_{i}. The coefficient of the isotropic part, d_{0}, is equal to τ_{NL}/6 discussed in the literature. A I ^{2}(φ)F^{2} interaction generates d_{2} = 2d _{0} which is, in turn, related to the quadrupole modulation parameter of the power spectrum, g_{*}, as d_{2} 14|g _{*}|N^{2} with N 60. We show that d_{0} and d_{2} can be equally well-constrained: the expected 68% CL error bars on these coefficients from a cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to ℓ_{max} = 2000 are δd_{2} 4δd_{0} = 105. Therefore, we can reach |g_{*}| = 10^{-3} by measuring the angle-dependent trispectrum. The current upper limit on τ_{NL} from the Planck temperature maps yields |g_{*}| < 0.02 (95% CL).

Original language | English (US) |
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Article number | 027 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2014 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2014 |

## Keywords

- CMBR theory
- Inflation
- Non-gaussianity
- Physics of the early universe