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

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 $\sum m_{\nu }=(0.357\pm 0.099)\mathrm{eV}$ and (ii) for a sterile neutrino $m_{\mathrm{sterile}}^{\mathrm{eff}}=(0.67\pm 0.18)\mathrm{eV}$ and $\Delta N_{\mathrm{eff}}=0.32\pm 0.20$. 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.

18 pages, 11 figures

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