# Super-CMB fluctuations and the Hubble tension

## TL;DR

This paper investigates how non-Gaussian covariance from primordial trispectrum affects CMB data analysis and can reduce the Hubble tension by allowing for extended models with additional parameters.

## Contribution

It demonstrates that including non-Gaussian covariance from primordial trispectrum can significantly alter cosmological parameter estimates and alleviate the Hubble tension.

## Key findings

- Non-Gaussian covariance can shift standard cosmological parameters.
- Extended models with trispectrum parameters improve fit to combined data.
- Likelihood improves by Δχ² ≈ -15 when including trispectrum effects.

## Abstract

We study the covariance in the angular power spectrum estimates of CMB fluctuations when the primordial fluctuations are non-Gaussian. The non-Gaussian covariance comes from a nonzero connected four-point correlation function -- or the trispectrum in Fourier space -- and can be large when long-wavelength (super-CMB) modes are strongly coupled to short-wavelength modes. The effect of such non-Gaussian covariance can be modeled through additional freedom in the theoretical CMB angular power spectrum and can lead to different inferred values of the standard cosmological parameters relative to those in $\Lambda$CDM. Taking the collapsed limit of the primordial trispectrum in the quasi-single field inflation model as an example, we study how the six standard $\Lambda$CDM parameters shift when two additional parameters describing the trispectrum are allowed. The reduced statistical significance of the Hubble tension in the extended model allows us to combine the {\it Planck} temperature data and the type Ia supernovae data from Panstarrs with the distance-ladder measurement of the Hubble constant. This combination of data shows strong evidence for a primordial trispectrum-induced non-Gaussian covariance, with a likelihood improvement of $\Delta \chi^2 \approx -15$ (with two additional parameters) relative to $\Lambda$CDM.