Inflationary Freedom and Cosmological Neutrino Constraints

TL;DR

The study probes whether freedom in the primordial power spectrum (PPS) biases cosmological constraints on neutrino properties. By modeling the PPS with a 20-node spline and jointly analyzing Planck-like CMB data, BOSS galaxy clustering, and $H_0$ measurements, it quantifies how PPS flexibility alters bounds on $Σm_ν$ and $N_{eff}$. The key finding is that PPS freedom significantly weakens CMB-only neutrino bounds, but combining CMB with low-redshift probes restores robust, PPS-independent limits, yielding $Σm_ν<0.18$ eV (95% CL) when all three data sets are used; allowing $N_{eff}$ weakens these bounds by about a factor of 1.7. The work highlights the importance of multiple transfer-function probes to break inflationary degeneracies and constrains sterile or extra relativistic species while showing no strong evidence for PPS deviations.

Abstract

The most stringent bounds on the absolute neutrino mass scale come from cosmological data. These bounds are made possible because massive relic neutrinos affect the expansion history of the universe and lead to a suppression of matter clustering on scales smaller than the associated free streaming length. However, the resulting effect on cosmological perturbations is relative to the primordial power spectrum of density perturbations from inflation, so freedom in the primordial power spectrum affects neutrino mass constraints. Using measurements of the cosmic microwave background, the galaxy power spectrum and the Hubble constant, we constrain neutrino mass and number of species for a model independent primordial power spectrum. Describing the primordial power spectrum by a 20-node spline, we find that the neutrino mass upper limit is a factor three weaker than when a power law form is imposed, if only CMB data are used. The primordial power spectrum itself is constrained to better than 10 % in the wave vector range $k \approx 0.01 - 0.25$ Mpc$^{-1}$. Galaxy clustering data and a determination of the Hubble constant play a key role in reining in the effects of inflationary freedom on neutrino constraints. The inclusion of both eliminates the inflationary freedom degradation of the neutrino mass bound, giving for the sum of neutrino masses $Σm_ν< 0.18$ eV (at 95 % confidence level, Planck+BOSS+$H_0$), approximately independent of the assumed primordial power spectrum model. When allowing for a free effective number of species, $N_{eff}$, the joint constraints on $Σm_ν$ and $N_{eff}$ are loosened by a factor 1.7 when the power law form of the primordial power spectrum is abandoned in favor of the spline parametrization.

Figures (8)

• Figure 1: The CMB temperature power spectrum is plotted with data points from Planck in red, from ACT in green and from SPT in magenta. The large green dots indicate the locations of the spline nodes. The blue (black) solid curve is the best-fit theory spectrum to the CMB data set in the case of a power law (free/splined) PPS, for fixed $\Sigma m_{\nu} = 0$ eV. The respective dashed curves show the best fit spectra for fixed $\Sigma m_{\nu} = 2.5$ eV. The freedom in the spline PPS can compensate for the neutrino mass to keep the power spectrum at $\ell > 10$ virtually the same as the zero mass case, showing how inflaton freedom affects neutrino constraints.
• Figure 2: The mean PPS node values are shown, including error bars. The black points and error bars indicate the fit to CMB data only, and the results in light red correspond to CMB + BOSS galaxy clustering (points slightly offset for clarity). The solid lines are the primordial power spectra corresponding to the node values shown. The dashed line is the best-fit power law spectrum to the CMB-only data, marginalized over other parameters.
• Figure 3: The posterior probability distributions of the cosmological parameters, including neutrino mass. Results for the CMB-only data combination are shown in black and those for CMB+BOSS in light red. The solid curves give the results with a free (splined) PPS, while the dashed curves indicate results for the power law case. The number of neutrino species is here fixed to the standard three.
• Figure 4: Posterior distribution, for the CMB-only data combination, of late-universe "observables" $H_0$ and $r_s/D_V(z=0.57)$, with $\Sigma m_\nu$ color coded. Here $r_s$ is the sound horizon scale and $D_V(z=0.57)$ an effective distance to $z=0.57$, as measured from the angle-averaged BAO scale in the BOSS CMASS sample. The contours indicate $68 \%$ and $95 \%$ confidence regions and the dashed lines indicate $1\sigma$ ranges from direct measurement of $H_0$ and $r_s/D_V$ (see text). Note that our analysis uses the full shape of the galaxy power spectrum rather than just the BAO measurement. Left: Power law PPS. Right: Splined PPS. Allowing more freedom in the PPS causes a broadening of the distribution, but retains the strong parameter (anti-)correlations so that the addition of a galaxy clustering and/or $H_0$ measurement will still tighten the neutrino mass constraint.
• Figure 5: The measured galaxy power spectrum of the BOSS CMASS sample is plotted as dots with error bars. The black data points are the only ones used in our analysis, spanning the range $k = 0.03 - 0.12\,h\,{\rm Mpc}^{-1}$. The solid curves (black for spline PPS, blue for power law PPS) represent the models that best fit the CMB-only data for fixed $\Sigma m_\nu=0$, while the dashed curves give the predictions by the models best fitting the CMB data for $\Sigma m_\nu = 2.5$ eV (same as in Figure \ref{['fig:pps cl mnu']}). The green dots again indicate the locations of the PPS spline nodes.