Super-CMB fluctuations and the Hubble tension

TL;DR

The paper shows that a collapsed-limit primordial trispectrum from quasi-single-field inflation can generate a non-Gaussian covariance in the CMB angular power spectrum, which in turn shifts ΛCDM parameters when data are analyzed jointly with distance-ladder H_0 and SNIa observations. By introducing a super-sample modulation parameter A_0 and a trispectrum parameter ε, the authors quantify how this non-Gaussian covariance biases A_s and H_0, alleviating part of the Hubble tension. Using Planck TT+τ priors and Bayesian model comparison, they find that Planck-only data mildly prefer the extended model, while adding H_0 and SNIa data yields a substantial improvement in fit (Δχ^2  -15) and moderate-to-strong evidence (ln B_{01}  -3.8) for Super-ΛCDM, with H_0 ≈ 69.9 ± 1.7 and A_0 ≈ -0.21. The results suggest the super-sample trispectrum as a viable, data-consistent explanation for part of the H_0 discrepancy and motivate direct non-Gaussianity tests in CMB and large-scale structure, while noting that newer data could shift these conclusions.

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 $Λ$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 $Λ$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 $Δχ^2 \approx -15$ (with two additional parameters) relative to $Λ$CDM.

Figures (3)

• Figure 1: The trispectrum amplitude $\tau_{\rm NL}$ as a function of $a=n_s-2\epsilon-1$ resulting in the given variance of $A_0$, plotted for $\langle A_0^2 \rangle = 0.04$ and $0.01$. The expression for the variance Eq. (\ref{['eq:var_A']}) diverges for $a \leq 0$ or $n_s-2\epsilon \leq 1$. The existing constraint on $\tau_{\rm NL}$ ($\lesssim \mathcal{O}(10^4)$Ade:2013ydcFeng:2015pva) implicitly assumes $\epsilon=0$ such that $a\leq 0$ for $n_s \leq 1$. As shown in the plot, for small values of $a$, $\tau_{\rm NL} \lesssim 10^4$ can produce a variance $\langle A_0^2 \rangle \simeq 0.04$ large enough to be consistent with the preferred value of $A_0\simeq -0.2$ in our data analysis.
• Figure 2: Marginalized 1D and 2D posterior distributions for the parameters describing the primordial fluctuations $\left\{\ln(10^{10}A_s), n_s, A_0, \epsilon \right\}$, along with $H_0$, for different choices of data and models. The red contours show the results for the base $\Lambda$CDM model using Planck data. Allowing for the non-Gaussian covariance significantly broadens and shifts the constraints on the primordial amplitude and spectral index (thin-line contours). Adding $H_0$ and SNIa data helps in constraining the parameters in the Super-$\Lambda$CDM model (blue contours). The gray line and bands in the lower panels show the measurement and uncertainty (1 and 2 $\sigma$) of the distance-ladder Hubble constant measurement from Riess:2018byc.
• Figure 3: Posterior distributions for other parameters of interest, $\Omega_m$, $\Omega_m h^2$, $\sigma_8$ and $\sigma_8 \Omega_m^{0.5}$; see also discussion in the text.