Non-Gaussianity from isocurvature perturbations

TL;DR

This work addresses how isocurvature perturbations can source significant non-Gaussianity in the early universe and imprint distinctive signatures in the CMB. It develops a formalism that relates non-Gaussianity in isocurvature modes, via coefficients $f_{Sij}$, to the curvature perturbation non-Gaussianity $f_{\rm NL}$, and translates these into observable CMB bispectra using transfer functions and the Sachs-Wolfe approximation. A key result is that, in the Sachs-Wolfe regime, the CMB non-Gaussianity parameter satisfies $f_{\rm NL}^{\Delta T} \approx \mathcal{O}(10^2) \times f_{\rm NL}$ when isocurvature is the dominant source of the bispectrum, with the signal peaking at large angular scales and possessing a distinct scale dependence compared to adiabatic models. The axion provides a concrete realization: even a subdominant axion CDM fraction can generate sizable non-Gaussianity if the inflationary scale is $H_{\rm inf} \sim 10^{9}-10^{11}$ GeV, while respecting isocurvature bounds. Overall, the paper offers a framework to test inflationary scenarios involving light fields (like the QCD axion) via CMB bispectrum measurements, potentially linking high-energy physics to observable cosmological signatures.

Abstract

We develop a formalism to study non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the CMB temperature fluctuations, which may be confirmed in future experiments, or possibly, even in the currently available observational data. As an explicit example, we consider the QCD axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H_{inf} = O(10^9 - 10^{11})GeV.

Figures (6)

• Figure 1: $b_{{\rm L} \ell}(r)$ (top) and $b_{{\rm NL} \ell}(r)$ (bottom) from numerical calculation. We show the cases of isocurvature initial conditions (solid red line) and adiabatic conditions (dashed green line). Here we have assumed $P_S(k)=P_\zeta(k)$. From left to right panels, $r$ is set to be $r = \tau_0-0.5\tau_*,\ \tau_0-\tau_*$ and $\tau_0-1.5\tau_*$, respectively. Note that $b_{{\rm L} \ell}$ is a dimensionless quantity, while $b_{{\rm NL} \ell}$ has the dimensionality of $(\hbox{length})^{-3}$.
• Figure 2: The reduced bispectra $\ell_2(\ell_2+1)\ell_3(\ell_3+1)b^{\rm NL,\ L,\ L}_{\ell_1 \ell_2 \ell_3}/(2\pi)^2$ (top) and $\ell_1(\ell_1+1)\ell_2(\ell_2+1)b^{\rm L,\ L,\ NL}_{\ell_1 \ell_2 \ell_3}/(2\pi)^2$ (bottom). To avoid complexity, we have fixed $(\ell_1, \ell_2)=(9,11)$ (left), $(99,101)$ (middle), $(199,201)$ (right) and varied $\ell_3$. The solid red line and dashed green line correspond to the cases with isocurvature and adiabatic initial conditions, separately. The unobservable multipoles are shown as shaded region. We have set $f_S = 1$.
• Figure 3: $f^{\Delta T}_{\rm NL}/f_{\rm NL}$ is plotted as a function of $\ell_3$ with various sets of $(\ell_1, \ell_2$). Only observable multipoles ($|\ell_1-\ell_2| \leq \ell_3 \leq \ell_1+ \ell_2$) are shown.
• Figure 4: Contours of $f_{\rm NL}=1,10$ and $100$ for $F_a = 10^{10}~$GeV. Gray shaded region is excluded from isocurvature constraint. In the blue region the PQ symmetry may be restored during inflation, and so, neither isocurvature fluctuation nor non-Gaussianity will arise. Also we show $r=10^{-4}$ by the green dash-dotted line.
• Figure 5: Same as Fig. \ref{['fig:NG-Fa10']} with $F_a = 10^{12}~$GeV. The upper shaded region is excluded from the axion overproduction.