Testing for New Physics: Neutrinos and the Primordial Power Spectrum

TL;DR

The paper investigates whether the inferred neutrino properties, specifically $\sum m_\nu$ and $N_\mathrm{eff}$, depend on the assumed form of the primordial power spectrum. It introduces a knot-spline reconstruction of the PPS with movable knots and uses Bayesian model selection to compare models with different PPS flexibility against standard $\Lambda$CDM, across Planck 2015, BAO, LRG, WiggleZ, SZ, and $H_0$ data. The main finding is that neutrino constraints are generally robust to PPS shape, with the strongest limit $\sum m_\nu \lesssim 0.13\ \mathrm{eV}$ arising from Planck15+LRG+BAO+$H_0$. Some tension among SZ, Planck, and $H_0$ data can induce PPS feature preferences, but these are interpreted as systematic biases rather than genuine new physics.

Abstract

We test the sensitivity of neutrino parameter constraints from combinations of CMB and LSS data sets to the assumed form of the primordial power spectrum (PPS) using Bayesian model selection. Significantly, none of the tested combinations, including recent high-precision local measurements of $\mathrm{H}_0$ and cluster abundances, indicate a signal for massive neutrinos or extra relativistic degrees of freedom. For PPS models with a large, but fixed number of degrees of freedom, neutrino parameter constraints do not change significantly if the location of any features in the PPS are allowed to vary, although neutrino constraints are more sensitive to PPS features if they are known a priori to exist at fixed intervals in $\log k$. Although there is no support for a non-standard neutrino sector from constraints on both neutrino mass and relativistic energy density, we see surprisingly strong evidence for features in the PPS when it is constrained with data from Planck 2015, SZ cluster counts, and recent high-precision local measurements of $\mathrm{H}_0$. Conversely combining Planck with matter power spectrum and BAO measurements yields a much weaker constraint. Given that this result is sensitive to the choice of data this tension between SZ cluster counts, Planck and $\mathrm{H}_0$ measurements is likely an indication of unmodeled systematic bias that mimics PPS features, rather than new physics in the PPS or neutrino sector.

Figures (8)

• Figure 1: (Left) The two-dimensional posterior distribution showing the $68\%$ and $95\%$ CI allowed regions in the $\sigma_8-\sum m_\nu$ plane for 0 knots and $\sum m_\nu$ free for various combinations of data. (Right) The same but for $N_\mathrm{eff}$ in the $h-N_\mathrm{eff}$ plane.
• Figure 2: Two-dimensional posterior distributions in the $\sigma_8-\sum m_\nu$ plane for 0 knots (solid line), 1 knot (dashed line), and 2 knots (dotted line) for various combinations of data sets. Models with more than 2 knots do not differ significantly from the $n=2$ case and are not displayed.
• Figure 3: $68\%$ and $95\%$ CI constraints on $N_\mathrm{eff}$ for models with $N_\mathrm{eff}$ allowed to vary and PPS reconstruction with knot location free. The data sets used are indicated in each panel (Planck15 is implicitly included in each panel).
• Figure 4: One-dimensional posterior distributions for $\sum m_\nu$ and $N_\mathrm{eff}$. The colors of the contours from darkest to lightest indicate increasing number of knots in the PPS from 0 to 2 knots. Higher numbers of knots do not lead to significant changes. All cases shown are for models where the knot location in $k$ is a free parameter.
• Figure 5: One-dimensional posterior distributions for $\sum m_\nu$ for (left) Planck15 only and (right) Planck15+BAO for the case of fixed knots. The color of line from dark to light represents increasing numbers of knots from 0 to 10 in intervals of 2.