Parity-violating CMB correlators with non-decaying statistical anisotropy

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 ℒ = 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*(k̂⋅Â)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 (k̂1 ⋅ k̂2) P(k1) P(k2) + 2 perms , with c0:c1:c2=2-3:1 (c1≠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 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 / ρϕ ≲ 10−9 at 0γ=. We find that the upper limit on the vector energy density becomes much more stringent as γ grows.