Impact of neutrino properties on the estimation of inflationary parameters from current and future observations

TL;DR

This paper analyzes how uncertainties in neutrino properties bias the estimation of inflationary parameters from CMB and BAO data. Using Bayesian MCMC with exact NH/IH hierarchies and alternative approximations, it shows that $M_ u$ and $N_ ext{eff}$ can shift the scalar spectral index $n_s$ by up to ~0.8$\sigma$ under nonstandard priors, though current data largely suppress these shifts, especially when BAO are included. The hierarchy itself has negligible impact, while improper minimal-mass priors (e.g., $M_ u=0$) can bias results; forecasts for COrE and Stage-IV indicate persistent, but manageable, neutrino-induced shifts in $n_s$ that could affect inflation-model discrimination. The work emphasizes the importance of marginalizing over neutrino properties in precision cosmology and demonstrates how neutrino physics can influence the interpretation of inflationary potentials in models like Natural Inflation and Higgs-like scenarios. Overall, careful treatment of neutrino sector uncertainties is crucial for robust constraints on inflation from future cosmological data.

Abstract

We study the impact of assumptions about neutrino properties on the estimation of inflationary parameters from cosmological data, with a specific focus on the allowed contours in the $n_s/r$ plane. We study the following neutrino properties: (i) the total neutrino mass $ M_ν=\sum_i m_i$; (ii) the number of relativistic degrees of freedom $N_{eff}$; and (iii) the neutrino hierarchy: whereas previous literature assumed 3 degenerate neutrino masses or two massless neutrino species (that do not match neutrino oscillation data), we study the cases of normal and inverted hierarchy. Our basic result is that these three neutrino properties induce $< 1 σ$ shift of the probability contours in the $n_s/r$ plane with both current or upcoming data. We find that the choice of neutrino hierarchy has a negligible impact. However, the minimal cutoff on the total neutrino mass $M_{ν,{min}}=0 $ that accompanies previous works using the degenerate hierarchy does introduce biases in the $n_s/r$ plane and should be replaced by $M_{ν,min}= 0.059$ eV as required by oscillation data. Using current CMB data from Planck and Bicep/Keck, marginalizing over $ M_ν$ and over $r$ can lead to a shift in the mean value of $n_s$ of $\sim0.3σ$ towards lower values. However, once BAO measurements are included, the standard contours in the $n_s/r$ plane are basically reproduced. Larger shifts of the contours in the $n_s/r$ plane (up to 0.8$σ$) arise for nonstandard values of $N_{eff}$. We also provide forecasts for the future CMB experiments COrE and Stage-IV and show that the incomplete knowledge of neutrino properties, taken into account by a marginalization over $M_ν$, could induce a shift of $\sim0.4σ$ towards lower values in the determination of $n_s$ (or a $\sim 0.8σ$ shift if one marginalizes over $N_{eff}$). Comparison to specific inflationary models is shown.

Figures (12)

• Figure 1: Colored scatter plot showing the mutual degeneracies between $n_s$, $H_0$ (in $\mathrm{km\,s^{-1}\,Mpc^{-1}}$) and $M_\nu$ (in $\,\mathrm{eV}$) for the $\Lambda\mathrm{CDM}+M_\nu$ model in the "3deg" case, i.e. a cosmological scenario with three massive and fully degenerate neutrinos. Each point represents a model in the $n_s/H_0$ plane. The color code represents different neutrino masses, according to the vertical bar on the right of the figure. The two-dimensional contours are for Planck TT+lowP (black) and Planck TT+lowP+BAO (red). The inclusion of BAO clearly excludes the high-mass region (red and yellow points) of the parameter space.
• Figure 2: Marginalized confidence intervals for the scalar spectral index $n_s$ for the indicated cosmological models and datasets. Solid bold lines are for the exact NH parameterization (total neutrino mass distributed according normal hierarchical scenario), solid light lines for the IH parameterization (total neutrino mass distributed according inverted hierarchical scenario), dashed lines for the degenerate parameterization (one massive neutrino plus two massless species when $M_\nu$ is fixed, three degenerate massive neutrinos when $M_\nu$ is allowed to vary). The two dashed-dotted blue lines are drawn for the NH parameterization when fixing the lightest eigenstate to $m_1=0.009\,\,\mathrm{eV}$ (first dashed-dotted line from the top) and $m_1=0.164\,\mathrm{eV}$ (second dashed-dotted blue line from the top), respectively. The vertical bands are 68% and 95% CL limits from Planck TT+lowP in the context of a $\Lambda\mathrm{CDM}$ model with one massive neutrino with mass $M_\nu=0.06\,\mathrm{eV}$.
• Figure 3: Two-dimensional probability contours at 68% and 95% CL in the $n_s-M_\nu$ plane for the Planck TT+lowP dataset and the $\Lambda\mathrm{CDM}+M_\nu$ model, when assuming three fully degenerate massive neutrinos (labeled as "3deg" scenario in the main text).
• Figure 4: Two-dimensional probability contours at 68% and 95% CL, and one-dimensional posterior probability distributions showing the main correlations among cosmological parameters responsible for the shift in $n_s$, for the indicated dataset and the $\Lambda\mathrm{CDM}+M_\nu$ model, when assuming three fully degenerate massive neutrinos (labeled as "3deg" scenario in the main text).
• Figure 5: Two-dimensional probability contours at 68% and 95% CL, and one-dimensional posterior probability distributions showing the main degeneracies among cosmological parameters responsible for the shift in $n_s$, for the indicated dataset and the $\Lambda\mathrm{CDM}+N_\mathrm{eff}+M_\nu$ model. In plotting the figure, we have assumed three massive degenerate neutrinos ("3deg" parameterization in the main text) and a broad prior on $N_\mathrm{eff}$ ($0\leq N_\mathrm{eff}\leq10$, see the text for further details about additional priors adopted on $N_\mathrm{eff}$).