Collective Symmetry Breaking and Resonant Non-Gaussianity

TL;DR

This work addresses how to sustain a nearly scale-invariant inflaton power spectrum while inducing large, oscillatory non-Gaussian features in the bispectrum. It introduces collective symmetry breaking of shift symmetries with extra fields and analyzes two regimes—perturbative QSFI and strong linear mixing—deriving explicit resonant bispectrum formulas that scale with the resonance-to-Hubble ratio $\alpha$ and with the couplings. The key finding is that radiative corrections can be suppressed so that oscillations are enhanced in the bispectrum without corresponding large oscillations in the power spectrum, though equilateral configurations exhibit substantial numerical suppression. The results indicate that bispectrum-dominated resonant signatures can be observable in principle, while highlighting the need for UV completion and careful assessment of CMB detectability and potential fine-tuning concerns.

Abstract

We study inflationary models that produce a nearly scale-invariant power spectrum while breaking scale invariance significantly in the bispectrum. Under most circumstances, such models are finely-tuned, as radiative corrections generically induce a larger signal in the power spectrum. However, when scale invariance is broken collectively (i.e., it requires more than one coupling to break the symmetry), these radiative corrections may be suppressed. We illustrate the features and limitations of collective symmetry breaking in the context of resonant non-gaussianity. We discuss two examples where oscillatory features can arise predominantly in the bispectrum.

Figures (3)

• Figure 1: The leading perturbative contributions to the power spectrum (left) and bispectrum (right) of the curvature perturbation $\zeta$ that arise in quasi-single-field inflation.
• Figure 2: Contour Plot for $\frac{\left(\frac{S}{N}\left(\left\langle \zeta^3 \right\rangle\right)\right)}{\left(\frac{S}{N}\left(\delta\left\langle \zeta^2 \right\rangle\right)\right)}$. To ensure reliable results for the small values of $\alpha$, the signal to noise includes the full $\alpha$ dependence of the bispectrum given by equation \ref{['equ:fullbispectrum']} (and similarly for the power spectrum). We have enforced $\alpha > 2$ to ensure that the our calculations and the theory are under control.
• Figure 3: Contour Plot for $\frac{\left(\frac{S}{N}\left(\left\langle \zeta^3 \right\rangle\right)\right)}{\left(\frac{S}{N}\left(\delta\left\langle \zeta^2 \right\rangle\right)\right)}$ with $\alpha \equiv \omega_\star / H =10$. The signal to noise from the bispectrum and the power spectrum was calculated using the full $\alpha$ dependence from equations \ref{['equ:bispec2']} and \ref{['equ:derivative']}.