Cosmological limits on the neutrino mass sum for beyond-$\Lambda$CDM models

The sum of cosmic neutrino masses can be measured cosmologically, as the sub-eV particles behave as `hot' dark matter whose main effect is to suppress the clustering of matter compared to a universe with the same amount of purely cold dark matter. Current astronomical data provide an upper limit on $\Sigma m_{\nu}$ between 0.07 - 0.12 eV at 95% confidence, depending on the choice of data. This bound assumes that the cosmological model is $\Lambda$CDM, where dark energy is a cosmological constant, the spatial geometry is flat, and the primordial fluctuations follow a pure power-law. Here, we update studies on how the mass limit degrades if we relax these assumptions. To existing data from the Planck satellite we add new gravitational lensing data from the Atacama Cosmology Telescope, the new Type Ia Supernova sample from the Pantheon+ survey, and baryonic acoustic oscillation (BAO) measurements from the Sloan Digital Sky Survey and the Dark Energy Spectrosopic Instrument. We find the neutrino mass limit is stable to most model extensions, with such extensions degrading the limit by less than 10%. We find a broadest bound of $\Sigma m_{\nu}<0.19 ~\rm{eV}$ at 95% confidence for a model with dynamical dark energy, although this scenario is not statistically preferred over the simpler $\Lambda$CDM model.