A New Window on Primordial non-Gaussianity

TL;DR

This work proposes using CMB μ-distortion to probe primordial perturbations at very small scales, $50 \lesssim k \lesssim 10^{4}$ Mpc$^{-1}$, outside the standard CMB/LSS window. It derives how μ arises from Silk damping energy injection and shows that μ–T cross-correlation and μ–μ auto-correlation isolate the local bispectrum in the squeezed limit and the trispectrum, respectively. A Fisher forecast for a PIXIE-like instrument suggests potential constraints on $f_{NL}^{\mathrm{loc}}$ at the level of $\Delta f_{NL} \sim 10^{3}$ (with possible stronger bounds for certain small-scale power or squeezed-limit scaling), highlighting μ-distortion as a clean, linear-physics probe with complementary information to conventional large-scale structure measurements. Overall, the paper argues that spectral distortions offer a promising avenue to constrain primordial non-Gaussianity at ultra-small scales, with the potential for strong, model-dependent enhancements and reduced cosmic variance in the $\mu T$ channel.

Abstract

We know very little about primordial curvature perturbations on scales smaller than about a Mpc. Measurements of the mu-type distortion of the CMB spectrum provide the unique opportunity to probe these scales over the unexplored range from 50 to 10^4 Mpc^-1. This is a very clean probe, in that it relies only on well-understood linear evolution. We point out that correlations between mu-distortion and temperature anisotropies can be used to test Gaussianity at these very small scales. In particular the mu-T cross correlation is proportional to the very squeezed limit of the primordial bispectrum and hence measures fNL^loc, while mu-mu is proportional to the primordial trispectrum and measures tauNL. We present a Fisher matrix forecast of the observational constraints.

Figures (1)

• Figure 1: The figure shows the power spectrum with Silk damping as function of $\log k$. The dotted, dashed and dot-dashed lines are $\Delta_{R}^{2}e^{-2k^{2}/k_{D}^{2}}$ at $z_{\mu,i}=2\times 10^{6}$, $z_{\mu,f}=5\times 10^{4}$ and $z_{L}=1100$ respectively. The red area on the right indicated by $\mu$ is the difference of the power spectrum between $z_{\mu,i}$ and $z_{\mu,f}$. Once integrated over $\log k$ this gives the $\mu$-distortion. For comparison on the left we have highlighted the scales probed by LSS and CMB anisotropies.