The implications of an extended dark energy cosmology with massive neutrinos for cosmological tensions

TL;DR

This paper investigates whether extended cosmologies that include massive neutrinos and an exotic, minimally constrained dark energy component can resolve the intertwined tensions in $H_0$, Ly-$\alpha$, and $S_8$. By analyzing a comprehensive suite of early- and late-Universe data and performing both a joint parameter extension and a non-parametric ExDE reconstruction, the authors find that a neutrino-mass sum around $0.4$ eV robustly improves $S_8$ when the $H_0$ tension is addressed, but the $H_0$ discrepancy is not fully resolved in any of the tested models. Allowing flexible ExDE dynamics reduces the tension to about $1.9\sigma$ with all datasets, though a negative ExDE density near $z\sim2.3$ appears data-driven and potentially systematic, particularly when Ly-$\alpha$ is included. The analyses consistently show that the $H_0$ tension persists unless one omits either galaxy BAO or JLA data, and that the neutrino mass remains constrained near $0.4$ eV in successful reconciliations, highlighting limitations of late-Universe modifications within GR and pointing toward potential new physics or data systematics in the current datasets.

Abstract

We perform a comprehensive analysis of the most common early- and late-Universe solutions to the $H_0$, Ly-$α$, and $S_8$ discrepancies. When considered on their own, massive neutrinos provide a natural solution to the $S_8$ discrepancy at the expense of increasing the $H_0$ tension. If all extensions are considered simultaneously, the best-fit solution has a neutrino mass sum of $\sim 0.4$ eV, a dark energy equation of state close to that of a cosmological constant, and no additional relativistic degrees of freedom. However, the $H_0$ tension, while weakened, remains unresolved. Motivated by this result, we perform a non-parametric reconstruction of the evolution of the dark energy fluid density (allowing for negative energy densities), together with massive neutrinos. When all datasets are included, there exists a residual $\sim1.9σ$ tension with $H_0$. If this residual tension remains in the future, it will indicate that it is not possible to solve the $H_0$ tension solely with a modification of the late-Universe dynamics within standard general relativity. However, we do find that it is possible to resolve the tension if either galaxy BAO or JLA supernovae data are omitted. We find that \textit{negative} dark energy densities are favored near redshift $z\sim2.35$ when including the Ly-$α$ BAO measurement (at $\sim 2σ$). This behavior may point to a negative curvature, but it is most likely indicative of systematics or at least an underestimated covariance matrix. Quite remarkably, we find that in the extended cosmologies considered in this work, the neutrino mass sum is always close to $0.4$ eV regardless of the choice of external datasets, as long as the $H_0$ tension is solved or significantly decreased.

Figures (4)

• Figure 1: The posterior distribution of $\{H_0,\sigma_8,\Omega_m,\sum m_\nu, w_0,w_a,\Delta N_\textrm{fluid}\}$ when fitting to all datasets considered in this work, compared to the $\Lambda$CDM fit of the same dataset.
• Figure 2: Reconstructed ExDE energy density and Hubble expansion rate (compared to the $\Lambda$CDM prediction from Planck TT,TE,EE+SIMlow, black line) with $\sum m_\nu=0.06~\mathrm{eV}$ (left panel) or $\sum m_\nu$ left as a free parameter (right panel), when including all datasets considered in this work and for different choice of prior on $\Omega_\mathrm{ExDE}$ (see text). The thick solid lines show the best fit spline in each case, while the thin lines show samples from the $68\%$ confidence region. The vertical arrows show the positions of the knots. The orange band indicates the uncertainty on the Hubble parameter as measured by SH0ES (strictly speaking it is only valid a $z=0$).
• Figure 3: Left panel: A comparison between the 1D and 2D posterior distributions of ($\sigma_8,\Omega_m,H_0,\sum m_\nu$) obtained in various models when using all datasets considered in this work. The grey band shows the R16 measurement, the purple band is the Planck SZ determination of $S_8$. Right panel: Reconstructed DE energy density and Hubble expansion rate (compared to the $\Lambda$CDM prediction from Planck TT,TE,EE+SIMlow, black line) with $\sum m_\nu$ left as a free parameter. We include either the BAO (red) or JLA data (blue). The thick solid lines show the best fit spline in each case, while the thin lines show draws from the $68\%$ most likely fits. The red arrows pointing upwards show the locations of the BAO knots, while the blue arrows pointing downwards show the positions of the JLA knots. The orange band indicates the uncertainty on the Hubble parameter as measured by SH0ES (strictly speaking it is only valid a $z=0$).
• Figure 4: 1D and 2D posterior distributions of ($\sigma_8,\Omega_m,H_0,\sum m_\nu$) with a fixed neutrino mass sum (left panel) and a free neutrino mass sum (right panel) when using SDSS DR7 CFHTLens, SH0ES, CMB, Ly-$\alpha$ BAO DR11, and either galaxy BAO DR12 (red curves) or JLA (blue curves). The grey band shows the SH0ES measurement, while the purple band is the Planck SZ determination of $S_8$.