Parity-violating CMB correlators with non-decaying statistical anisotropy

Nicola Bartolo; Sabino Matarrese; Marco Peloso; Maresuke Shiraishi

doi:10.1088/1475-7516/2015/07/039

paper

Parity-violating CMB correlators with non-decaying statistical anisotropy

arXiv:1505.02193 · doi:10.1088/1475-7516/2015/07/039

Abstract

We examine the cosmological correlators induced by the simultaneous breaking of parity and of statistical isotropy, e.g., in presence of the coupling $L = f (ϕ) (- \frac{1}{4} F^{2} + \frac{γ}{4} F F ~)$ 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, $P_{ζ} (k) = P (k) [1 + g_{*} (k^\cdot A^)^{2}]$ , and a (angle-averaged) scalar bispectrum that is a linear combination of the first $3$ Legendre polynomials, $B_{ζ} (k_{1}, k_{2}, k_{3}) = \sum_{L} c_{L} P_{L} (k^_{1} \cdot k^_{2}) P (k_{1}) P (k_{2}) + 2 perms$ , with $c_{0} : c_{1} : c_{2} = 2 : - 3 : 1$ ( $c_{1} \neq = 0$ is a consequence of parity violation, corresponding to the constant $γ \neq = 0$ ). 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 $⟨ a_{ℓ_{1} m_{1}} a_{ℓ_{2} m_{2}}^{*} ⟩$ , 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 $ρ_{A} / ρ_{ϕ} ≲ 1 0^{- 9}$ at $γ = 0$ . We find that the upper limit on the vector energy density becomes much more stringent as $γ$ grows.

23 pages, 2 figures. Abstract abridged. Accepted for publication in JCAP

Parity-violating CMB correlators with non-decaying statistical anisotropy

Abstract

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