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 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(k₁, k₂, k₃) = ∑_L c_L P_L (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 a_ℓ1m1a∗_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 ρ_A / ρ_φ10^-9 at 0γ=. We find that the upper limit on the vector energy density becomes much more stringent as γ grows.