Neutrino mass tension or suppressed growth rate of matter perturbations?

TL;DR

The paper investigates whether the cosmological neutrino-mass tension can be alleviated by allowing nonstandard growth of structure rather than modifying the background expansion. By introducing a constant growth index $\gamma$ and jointly varying $\sum m_{\nu}$ and $\gamma$ in analyses of Planck-PR4 (two high-$\ell$ likelihoods), DESI BAO, and Pantheon+ SN data, the authors show that neutrino mass bounds relax significantly while $\Omega_m$ stays near the standard value and the data prefer $\gamma>0.55$. This creates a $\gamma$–$\sum m_{\nu}$ degeneracy that can accommodate terrestrial neutrino bounds, but at the cost of departing from canonical $\Lambda$CDM growth; stronger priors (e.g., NO ordering) strengthen the preference for larger $\gamma$. The work highlights the importance of perturbation-level physics in interpreting neutrino mass constraints and suggests that future data and more detailed growth models are needed to fully resolve the tension. Overall, nonstandard growth offers a complementary path to reconcile cosmology with particle physics without invoking background evolution changes like dynamical dark energy.

Abstract

Assuming a minimal $Λ$CDM cosmology with three massive neutrinos, the joint analysis of Planck cosmic microwave background data, DESI baryon acoustic oscillations, and distance moduli measurements of Type Ia supernovae from the Pantheon+ sample sets an upper bound on the total neutrino mass, $\sum m_ν\lesssim 0.06$-$0.07$ eV, that lies barely above the lower limit from oscillation experiments. These constraints are mainly driven by mild differences in the inferred values of the matter density parameter across different probes that can be alleviated by introducing additional background-level degrees of freedom (e.g., by dynamical dark energy models). However, in this work we explore an alternative possibility. Since both $Ω_\mathrm{m}$ and massive neutrinos critically influence the growth of cosmic structures, we test whether the neutrino mass tension may originate from the way matter clusters, rather than from a breakdown of the $Λ$CDM expansion history. To this end, we introduce the growth index $γ$, which characterizes the rate at which matter perturbations grow. Deviations from the standard $Λ$CDM value ($γ\simeq 0.55$) can capture a broad class of models, including non-minimal dark sector physics and modified gravity. We show that allowing $γ$ to vary significantly relaxes the neutrino mass bounds to $\sum m_ν\lesssim 0.13$-$0.2$ eV, removing any tension with terrestrial constraints without altering the inferred value of $Ω_\mathrm{m}$. However, this comes at the cost of departing from standard growth predictions: to have $\sum m_ν\gtrsim 0.06$ eV one needs $γ> 0.55$, and we find a consistent preference for $γ> 0.55$ at the level of $\sim 2σ$. This preference increases to $\sim 2.5$-$3σ$ when a physically motivated prior $\sum m_ν\ge 0.06$ eV from oscillation experiments is imposed.

Figures (6)

• Figure 1: CMB temperature, polarization and cross-correlation power spectra for different values of the total neutrino mass (left panels), and for different values of the growth index $\gamma$ (right panels), see text for details.
• Figure 2: Matter power spectrum at redshift $z = 1.5$ for a standard growth scenario ($\gamma = 0.55$, dashed lines) and a modified one with $\gamma = 0.7$ (solid lines). The different colors depict different values of the total neutrino mass, namely $\sum m_\nu = 0.06$, $0.1$, and $0.3$ eV. In the bottom panel, we show the ratios of the power spectra for the different parameter cases relative to the $\Lambda$CDM model.
• Figure 3: One-dimensional marginalized posterior distributions and two-dimensional 68% and 95% CL contours in the ($\gamma$, $\sum m_\nu$) plane for different Planck CMB likelihoods combined with DESI and PP data. The horizontal black dashed line labeled “NO” marks the lower bound on the total neutrino mass set by oscillation experiments ($\sum m_\nu > 0.06$ eV). Values below this line are therefore in tension with oscillation data. Instead, the horizontal black dashed line labeled “IO” indicates the lowest value of the total neutrino mass compatible with the inverted ordering ($\sum m_\nu > 0.1$ eV). If the total neutrino mass lies between the NO and IO lines, only the normal ordering is allowed, whereas for values above the IO line both orderings remain viable. The vertical black dashed line corresponds to the standard prediction for the growth index ($\gamma \simeq 0.55$).
• Figure 4: One-dimensional marginalized posterior distributions and two-dimensional 68% and 95% CL probability contours for $\gamma$ and $S_8$ (top panels) and $\gamma$ and $H_0$ (bottom panels) for the different Planck CMB likelihoods combined with DESI and PP. The horizontal black dashed line corresponds to the standard prediction for the growth index, $\gamma \simeq 0.55$.
• Figure 5: One-dimensional marginalized posterior distributions and two-dimensional 68% and 95% CL contours for several cosmological parameters of interest, obtained from the analysis of Plik+DESI+PP under the different cosmological models and prior choices indicated in the figure legend. The dashed grey lines denote the lower bound on the total neutrino mass from oscillation experiments ($\sum m_\nu \simeq 0.06$ eV) and the standard $\Lambda$CDM prediction for the growth index ($\gamma = 0.55$).