## Abstract

We examine the effect induced on cosmological correlators by the simultaneous breaking of parity and of statistical isotropy. As an example of this, we compute the scalar-scalar, scalar-tensor, tensor-tensor and scalar-scalar-scalar cosmological correlators in presence of the coupling = f(φ) ( - 1/4 F^{2} + γ/4 F F ) between the inflaton φ and a vector field with vacuum expectation value A. For a suitably chosen function f, the energy in the vector field ρ_{A} does not decay during inflation. This results in nearly scale-invariant signatures of broken statistical isotropy and parity. Specifically, we find that the scalar-scalar correlator of primordial curvature perturbations includes a quadrupolar anisotropy, P_{ζ}(k) = P(k)[1+g_{∗}(cÂ)^{2}], and a (angle-averaged) scalar bispectrum that is a linear combination of the first 3 Legendre polynomials, B_{ζ}(k_{1}, k_{2}, k_{3}) = ∑_{L} c_{L} P_{L} (_{1} c _{2}) P(k_{1}) P(k_{2}) + 2 perms , with c_{0}:c_{1}:c_{2}=2-3:1 (c_{1}0 is a consequence of parity violation, corresponding to the constant 0γ ). The latter is one of the main results of this paper, which provides for the first time a clear example of an inflationary model where a non-negligible c_{1} contribution to the bispectrum is generated. The scalar-tensor and tensor-tensor correlators induce characteristic signatures in the Cosmic Microwave Background temperature anisotropies (T) and polarization (E/B modes); namely, non-diagonal contributions to a_{ℓ1m1}a∗_{ℓ2m2}, with |ℓ_{1} - ℓ_{2}| = 1 in TT, TE, EE and BB, and |ℓ_{1} - ℓ_{2}| = 2 in TB and EB. The latest CMB bounds on the scalar observables (g_{∗}, c_{0}, c_{1} and c_{2}), translate into the upper limit ρ_{A} / ρ_{φ}10^{-9} at 0γ=. We find that the upper limit on the vector energy density becomes much more stringent as γ grows.

Original language | English (US) |
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Article number | 039 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2015 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2015 |

### Bibliographical note

Publisher Copyright:© 2015 IOP Publishing Ltd and Sissa Medialab srl .

## Keywords

- axions
- cosmological perturbation theory
- inflation
- non-gaussianity