Changing the prior: absolute neutrino mass constraints in nonlocal gravity

TL;DR

This work revisits the Planck+SNIa+BAO constraints that previously disfavored the nonlocal RR gravity model, attributing the tension to a late-time phantom dark-energy component that shifts the $H_0$–$Ω_m$ relation. By extending the neutrino sector to three degenerate masses and treating $\sum m_\nu$ as a free parameter, the authors reveal a degeneracy between massive neutrinos and nonlocal gravity effects, substantially mitigating the tension and making the $\nu RR$ model statistically equivalent to its neutrino-extended $\nu\Lambda{\rm CDM}$ counterpart under current data. The analysis finds evidence for a nonzero $\sum m_\nu$ at ~2σ in the $\nu RR$ framework, with a best-fit around $0.21$ eV, and shows improved compatibility with growth-rate measurements when neutrinos are allowed to be massive. This illustrates the model-dependence of absolute neutrino mass constraints and underscores the potential of upcoming galaxy surveys to disentangle modified gravity from neutrino effects.

Abstract

Prior change is discussed in observational constraints studies of nonlocally modified gravity. In the latter, a model characterized by a modification of the form $\sim m^2 R\Box^{-2}R$ to the Einstein-Hilbert action was compared against the base $Λ$CDM one in a Bayesian way. It was found that the competing modified gravity model is significantly disfavored (at $22 \,$:$\, 1$ in terms of betting-odds) against $Λ$CDM given CMB+SNIa+BAO data, because of a dominant tension appearing in the $H_0 \,$-$\, Ω_M$ plan. We identify the underlying mechanism generating such a tension and show that it is mostly caused by the late-time, quite smooth, phantom nature of the effective dark energy described by the nonlocal model. We find possible solutions for it to be resolved and explore a given one that consists in extending the initial baseline from one massive neutrino eigenstate to three degenerate ones, whose absolute mass $\sum m_ν\, / \, 3$ is allowed to take values within a reasonable prior interval. As a net effect, the absolute neutrino mass is inferred to be non-vanishing at $2 σ$ level, best-fitting at $\sum m_ν\approx 0.21 {\, \rm eV}$, and the Bayesian tension disappears rendering the nonlocal gravity model statistically equivalent to $Λ$CDM, given recent CMB+SNIa+BAO data. We also discuss constraints from growth rate measurements $f σ_8$ whose fit is found to be improved by a larger massive neutrino fraction as well. The $ν$-extended nonlocal model also prefers a higher value of $H_0$ than $Λ$CDM, therefore in better agreement with local measurements.

Figures (4)

• Figure 1: Hubble expansion rate (top), CMB temperature power spectrum (middle) and CMB lensing power spectrum (bottom) for a few illustrative $RR$ cosmologies, plotted as the relative difference to the best-fitting $\Lambda{\rm CDM}$ cosmology to the Planck dataset. The red curve displays the prediction of the best-fitting $RR$ model to the Planck dataset. The green curves show the prediction of the $RR$ gravity model with the same parameters as the best-fitting $\Lambda{\rm CDM}$ model to Planck data. The remainder curves show the same as the green ones, but with $H_0 = 71.31 {\rm km/s/Mpc}$ (blue) and $\sum m_\nu = 0.423\ {\rm eV}$ (cyan), which have been adjusted to yield the same angular acoustic scale $\theta_* = 0.010414$ as $\Lambda{\rm CDM}$. In the middle and lower panels, the grey symbols with errorbars show the power spectra as measured by the Planck satellite Ade:2015xua.
• Figure 2: Two dimensional marginalized constraints on the $H_0-\Omega_{m}$ plane in the $\Lambda{\rm CDM}$ (top) and $RR$ (bottom) models obtained with the Planck (red), BAO (green) and JLA (grey) datasets. The blue contours are the same as the red ones, but for constraints in which $\sum m_\nu$ is a free parameter. For fixed color, the two contour shades indicate $1\sigma$ and $2\sigma$ confidence level. The BAO and JLA contours do not change appreciably when $\sum m_\nu$ varies so we do not display them explicitly.
• Figure 3: One and two dimensional marginalized constraints on the parameters $\sum m_\nu$, $\sigma_8$ and $\Omega_{m}$ in the $\nu RR$ and $\nu\Lambda{\rm CDM}$ models, obtained with the Planck and BAPJ datasets, as labelled. For fixed color, the two contour shades indicate $1\sigma$ and $2\sigma$ limits.
• Figure 4: Time evolution of the growth rate $f\sigma_8$ for the best-fitting $\Lambda{\rm CDM}$, $RR$ and $\nu RR$ models to the BAPJ dataset. For the case of the $\nu RR$ model (red), the solid and dashed lines display the result at $k = 0.01\ h/{\rm Mpc}$ and $k = 0.5\ h/{\rm Mpc}$, respectively. For the $\Lambda{\rm CDM}$ and $RR$ models the growth rate is scale-independent (apart from the very small scale-dependency induced by the small neutrino fraction, $\sum m_\nu = 0.06\ {\rm eV}$). The grey symbols show the observational determination from the final BOSS DR12 release Alam:2016hwk. The black symbols show the forecasted precision for Euclid, centered around the $\Lambda{\rm CDM}$ result.