Constraints on neutrino mass and dark energy agnostic to the sound horizon

TL;DR

This work investigates neutrino mass and dark-energy constraints while remaining agnostic to the sound horizon at recombination. By using uncalibrated inverse distance ladder methods and compressed geometric data, the authors show that dark energy evolution is well constrained and that large $H_0$ values are compatible with small sound horizons, leading to a substantially relaxed bound on the summed neutrino mass $ umu$ that can accommodate both normal and inverted hierarchies. The analysis demonstrates that priors on the primordial spectrum or full CMB high-$ ext{l}$ information are not essential for these conclusions, and that incorporating lab-based priors like KATRIN can yield concrete, consistent bounds such as $ umu=0.69^{+0.33}_{-0.47}$ eV, $r_s=131.1^{+6.8}_{-6.9}$ Mpc, and $H_0=74.7^{+3.4}_{-4.4}$ km/s/Mpc (68% CL). Overall, the approach highlights how relaxing early-Universe assumptions affects cosmological inferences and their compatibility with terrestrial measurements, while still constraining dark energy through geometry and growth observables.

Abstract

Recent BAO observations from DESI DR2 either hint at a possible dynamical dark energy component, which would worsen the Hubble tension, or at a 95\% credible interval for the summed neutrino mass hardly compatible with neutrino oscillation experiments. In this context, it is interesting to investigate constraints on neutrino masses, dark energy and the Hubble parameter that are agnostic to some aspects of the cosmological model. Here we choose to be agnostic to the value of the sound horizon at recombination, while sticking to standard assumptions regarding the time of recombination and the growth of structures. To be consistent, we also disregard information on the full shape of the CMB temperature and polarization spectrum on sub-degree scale. With such agnostic and conservative assumptions, using data mainly on uncalibrated distances, the growth of structures, and laboratory bounds on tritium $β$-decay, we find that: (i) the dark energy evolution is well constrained by uncalibrated data on angular and luminosity distances, with a mild preference for dynamical dark energy, independently of the value of the sound horizon; (ii) large values of the Hubble rate are favored, $H_0=74.7^{+3.4}_{-4.4}$ km/s/Mpc (68\%CL), together with low values of the sound horizon, $r_{\rm s}=131.1^{+6.8}_{-6.9}$ Mpc (68\%CL); the SH0ES value of $H_0$ is thus marginally preferred over the low value returned by the standard inverse distance ladder analysis; (iii) the cosmological neutrino mass bound relaxes to $\sum m_ν= 0.69^{+0.33}_{-0.47}$ eV (68\%CL) and becomes well compatible with the normal and inverted neutrino mass schemes.

Figures (6)

• Figure 1: Assuming a $\Lambda$CDM model with a free sound horizon and fixed values of $(\omega_{\rm b}, A_{\rm s}, n_{\rm s})$, 68% confidence contours for ($r_{\rm s}$, $\Omega_{\rm m}$, $H_0$) with different data sets (see legend and text).
• Figure 2: Assuming the $\Lambda$CDM+$\sum m_{\nu}$ model w/o a free sound horizon, triangle plot for ($H_0$, $M_B$, $r_{\rm s}$, $\Omega_{\rm m}$, $\sum m_\nu$) for different data sets (see legend and text), marginalized over ($\omega_{\rm b}$, $\omega_{\rm cdm}$, $A_{\rm s}$, $n_{\rm s}$).
• Figure 3: Assuming a $w_0 w_a$CDM+$\sum m_{\nu}$ model w/o a free sound horizon, triangle plot for ($H_0$, $w_0$, $w_a$, $M_B$, $r_{\rm s}$, $\Omega_{\rm m}$, $\sum m_\nu$) for different data sets (see legend and text), marginalized over ($\omega_{\rm b}$, $\omega_{\rm cdm}$, $A_{\rm s}$, $n_{\rm s}$).
• Figure 4: Assuming the $\Lambda$CDM model with a free sound horizon but fixed values of ($A_{\rm s}$, $n_{\rm s}$, $\omega_{\rm b}$, $\sum m_\nu$), 2D contours on the free parameters $(H_0, \omega_{\rm ncdm})$ inferred from the uncalibrated IDL likelihood, implemented either with Method I or Method II (see section \ref{['sec:agnostic']}). In both cases, $r_{\rm s}$ is floated freely and marginalised over (either implicitly or explicitly).
• Figure 5: Assuming a $\Lambda$CDM+$\sum m_{\nu}$ model w/o a free sound horizon, triangle plot for ($H_0$, $M_B$, $r_{\rm s}$, $\Omega_{\rm m}$, $\sum m_\nu$) for different data sets (see legend and text), marginalized over ($\omega_{\rm b}$, $\omega_{\rm cdm}$, $A_{\rm s}$, $n_{\rm s}$).