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

TL;DR

This study tackles the persistent discrepancy between the amplitude of density perturbations inferred from the CMB on large scales and direct LSS measurements on small scales within the ΛCDM framework. By jointly analyzing Planck or WMAP+SPT/ACT with SZ clusters, lensing, and RSD data, the authors quantify a strong CMB–LSS tension and explore extensions involving massive neutrinos and other explanations. They find that including active or sterile neutrinos can alleviate the tension to about 2–2.5σ, but at the cost of a degraded Planck fit, and no single model fully resolves the discrepancy; Bayesian evidence moderately favors extensions but remains sensitive to priors. The work highlights the potential of neutrino physics to reconcile datasets while underscoring the role of future high-precision CMB polarization and LSS measurements in resolving whether new physics is required.

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 $\sum m_ν= (0.357\pm0.099)\,{\rm eV}$ and (ii) for a sterile neutrino $m_{\rm sterile}^{\rm eff}= (0.67\pm0.18)\,{\rm eV}$ and $ΔN_{\rm eff}= 0.32\pm0.20$. This is, however, at the expense of a degraded fit to $Planck$ temperature data, and we quantify the residual tension at $2.5σ$ and $1.6 σ$ 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.

Figures (11)

• Figure 1: The quadrupole component of the redshift space power spectrum for the range of allowed Planck cosmologies (indicated by the narrow red and black bands), relative to the best-fit BOSS spectrum, for the North and South Galactic Caps (NGC and SGC respectively).
• Figure 2: Constraints on the $\sigma_8-\Omega_{\rm m}$ plane for LSS data only with Planck priors on $\Theta_{\rm MC}$ and $n_{\rm S}$ to avoid over-fitting the data. 1 and $2\sigma$ contours are shown for RSD (red), SZ clusters with $1-b = [0.7,1.0]$ (gold) and lensing (blue). The joint LSS constraint (LSSall, green) comes from combining the 3 different LSS probes.
• Figure 3: The putative tension between CMB and LSS measurements. The left-hand plot shows the constraint on $\sigma_8-\Omega_{\rm m}$, where the LSSall contour (green) is as shown in Fig. \ref{['fig:omegam_sigma8_lss']}, and Planck+WP+BAO (orange) and WMAP+highL+BAO (purple). It is clear that there is a discrepancy with the CMB and the joint LSS constraints on this parameter combination. The right-hand plot shows the $H_0-\Omega_{\rm m}$ plane for the same data, where the tension is even more apparent.
• Figure 4: Each panel shows the same data as those presented in in Fig. \ref{['fig:omegam_sigma8']} but with the inclusion of (i) $\sum m_{\nu}$ in the left column, and (ii) $m_{\rm sterile}^{\rm eff}$ and $\Delta N_{\rm eff}$ in the middle column. The right hand column shows Planck with RSD, lensing and SZ without WP (dark orange), where $\tau_{\rm R}$ is allowed to vary. The top row shows the reduction in tension in the $\sigma_8-\Omega_{\rm m}$ plane with the addition of each piece of "new physics", whilst the bottom row shows the $\sigma_8-H_0$ plane. It is clear that the possible values of $H_0$ allowed by LSS increases drastically when either active or sterile neutrinos are added.
• Figure 5: Comparison of the the 1D marginalised value $\sum m_{\nu}$ and $1\sigma$ errors for a wide range of LSS data combinations with CMB data. The CMB data used is Planck+WP (black) or WMAP+highL (red). In some cases there is clearly only an upper bound, but as the number of LSS datasets included increases the constraint stabilises to a non-zero value with a significance of around $3-4\sigma$. It is clear that preference for non-zero $\sum m_{\nu}$ is not dependent on this choice when two or more LSS datasets are included. Moreover, it is clear that there is a preference for non-zero neutrino mass without including SZ data.