Tension between the power spectrum of density perturbations measured on large and small scales

TL;DR

This paper investigates the persistent tension between large-scale and small-scale measurements of the density perturbation power spectrum, exploring neutrino mass and other modifications as potential solutions, and quantifies the residual discrepancies.

Contribution

It demonstrates the robustness of the tension across multiple datasets and evaluates the impact of massive neutrinos and other modifications on reconciling observations.

Findings

Tension exists between CMB and LSS measurements of the power spectrum.

Massive neutrinos can partially alleviate the tension but worsen the fit to CMB data.

Residual tension remains at 2.5 sigma even with neutrino inclusion.

Abstract

There is a tension between measurements of the amplitude of the power spectrum of density perturbations inferred using the Cosmic Microwave Background (CMB) and directly measured by Large-Scale Structure (LSS) on smaller scales. We show that this tension exists, and is robust, for a range of LSS indicators including clusters, lensing and redshift space distortions and using CMB data from either $Planck$ or WMAP+SPT/ACT. One obvious way to try to reconcile this is the inclusion of a massive neutrino which could be either active or sterile. Using $Planck$ and a combination of all the LSS data we find that (i) for an active neutrino $\sum m_{\nu}= (0.357\pm0.099)\,{\rm eV}$ and (ii) for a sterile neutrino $m_{\rm sterile}^{\rm eff}= (0.67\pm0.18)\,{\rm eV}$ and $\Delta N_{\rm eff}= 0.32\pm0.20$. This is, however, at the expense of a degraded fit to $Planck$ temperature data, and we quantify the residual tension at $2.5\sigma$ and $1.6 \sigma$ for massive and sterile neutrinos respectively. We also consider alternative explanations including a lower redshift for reionization that would be in conflict with polarisation measurements made by WMAP and $ad$-$hoc$ modifications to primordial power spectrum.