Non-Gaussian Enhancements of Galactic Halo Correlations in Quasi-Single Field Inflation

TL;DR

The paper develops analytic methods for quasi-single field inflation with a kinetically mixed inflaton–isocurvaton system to compute curvature perturbation correlators up to six points in the regime $m/H, μ/H \ll 1$. It then maps these primordial non-Gaussianities onto large-scale structure observables, deriving the halo power spectrum and bispectrum within a threshold bias model and identifying a scale-dependent bias that grows on very large scales. The authors provide explicit expressions for the two-, three-, four-, five-, and six-point functions of the curvature perturbation and show how these feed into halo statistics, predicting pronounced non-Gaussian enhancements at scales around $q \sim 0.005\,h\,\mathrm{Mpc}^{-1}$ for plausible parameter choices. These results offer testable predictions for upcoming large-scale structure surveys and clarify how primordial non-Gaussianity propagates into biased tracers like galactic halos.

Abstract

We consider a quasi-single field inflation model in which the inflaton interacts with a massive scalar field called the isocurvaton. Due to the breaking of time translational invariance by the inflaton background, these interactions induce kinetic mixing between the inflaton and isocurvaton, which is parameterized by a constant $μ$. We derive analytic formulae for the curvature perturbation two-, three-, four-, five-, and six-point functions explicitly in terms of the external wave-vectors in the limit where $μ$ and the mass of the isocurvaton $m$ are both much smaller than $H$. In previous work, it has been noted that when $m/H$ and $μ/H$ are small, the non-Gaussianities predicted by quasi-single field inflation give rise to long wavelength enhancements of the power spectrum for biased objects (e.g., galactic halos). We review this calculation, and calculate the analogous enhanced contribution to the bispectrum of biased objects. We determine the scale at which these enhanced terms are larger than the Gaussian piece. We also identify the scaling of these enhanced parts to the $n$-point function of biased objects.

Figures (12)

• Figure 1: Diagrams that contribute to three- and four-point correlations of $\zeta$ in the squeezed and collapsed limits respectively. These diagrams contribute to the galactic halo power spectrum. Dashed lines represent $\pi$, while solid lines represent $s$.
• Figure 2: Diagrams that contribute to the three-, four-, five-, and six-point correlations of $\zeta$ in the kinematic regimes that contribute to the enhanced part of the galactic halo bispectrum. Dashed lines represent $\pi$, while solid lines represent $s$.
• Figure 3: A diagrammatic representation of terms contributing to the galactic halo power spectrum. Cf. Fig. \ref{['fig:feynman 2 pt']}.
• Figure 4: A diagrammatic representation of terms contributing to the galactic halo bispectrum. Cf. Fig. \ref{['fig:feynman 3 pt']}.
• Figure 5: We plot the ratio of the galactic halo power spectrum in quasi-single field inflation to the halo power spectrum in which there are no primordial non-Gaussianities for a range of $\alpha_{-}$: $\alpha_-=0.025$ (lightest), $0.050$, $0.075$, $0.100$, $0.125$, $0.150$ (darkest). We plot for $\mu=m$ and $f_{NL}=10$ (green) and $f_{NL}=-10$ (purple).