Parity-violating CMB correlators with non-decaying statistical anisotropy

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 F2 + 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 ρA 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, Pζ(k) = P(k)[1+g∗(cÂ)2], and a (angle-averaged) scalar bispectrum that is a linear combination of the first 3 Legendre polynomials, Bζ(k1, k2, k3) = ∑L cL PL (1 c 2) P(k1) P(k2) + 2 perms , with c0:c1:c2=2-3:1 (c10 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 c1 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 aℓ1m1a∗ℓ2m2, with |ℓ1 - ℓ2| = 1 in TT, TE, EE and BB, and |ℓ1 - ℓ2| = 2 in TB and EB. The latest CMB bounds on the scalar observables (g∗, c0, c1 and c2), translate into the upper limit ρA / ρφ10-9 at 0γ=. We find that the upper limit on the vector energy density becomes much more stringent as γ grows.