Parity Violating Statistical Anisotropy

TL;DR

This work shows that a light Abelian vector field with a time-varying kinetic function and an axial coupling can produce scale-invariant, parity-violating spectra for its transverse modes. When such a vector feeds the curvature perturbation through the vector curvaton mechanism, parity violation emerges mainly in the bispectrum (via anisotropic $f_{\rm NL}$), while the power spectrum remains quadrupole-modulated. The authors derive conditions for scale invariance and parity violation, compute exact $f_{\rm NL}$ templates in multiple shapes, and discuss two concrete particle-theory realizations (string-inspired and orthogonal axion) illustrating viable parameter spaces. The results identify observational signatures that could reveal axial couplings in beyond-Standard-Model physics, notably parity-violating non-Gaussianity in the CMB bispectrum while respecting Planck-like bounds on statistical anisotropy.

Abstract

Particle production of an Abelian vector boson field with an axial coupling is investigated. The conditions for the generation of scale invariant spectra for the vector field transverse components are obtained. If the vector field contributes to the curvature perturbation in the Universe, scale-invariant particle production enables it to give rise to statistical anisotropy in the spectrum and bispectrum of cosmological perturbations. The axial coupling allows particle production to be parity violating, which in turn can generate parity violating signatures in the bispectrum. The conditions for parity violation are derived and the observational signatures are obtained in the context of the vector curvaton paradigm. Two concrete examples are presented based on realistic particle theory.

Figures (1)

• Figure 1: A log-log graph illustrating a possible evolution of the physical momentum $k/a$ and the function $Q\propto a^{c}$ during inflation (for a fixed $k$). Horizontal lines represent four possible cases for the value of the Hubble parameter. The end of inflation at $a=a_{\rm e}$ is depicted by a vertical dot-dashed line. The mode $k$ exits the horizon when the blue (solid) line crosses the dotted line. The four possible cases are the following. In the Case I the function $Q\ll H$ during inflation, no matter if it is increasing of decreasing. The Case II is when a function $Q\gg H$ before the mode exits the horizon, but becomes smaller than $H$ towards the end of inflation. This can only happen if $Q$ is a decreasing function of time. The Case III depicts a situation, when $Q\ll H$ before horizon exit, but $Q_{\mathrm{e}}\gg H$ at the end of inflation. This only is possible if $Q$ is an increasing function of time. Finally, in the Case IV $Q\gg H$ for both increasing and decreasing $Q$ during inflation. The black dots in the graph highlights the moment when $k/a_{\mathrm{x}}H=Q$.