Observable Predictions for Massive-Neutrino Cosmologies with Model-Independent Dark Energy

We investigate the bounds on the sum of neutrino masses in a cosmic-acceleration scenario where the equation of state $w(z)$ of dark energy (DE) is constructed in a model-independent way, using a basis of principal components (PCs) that are allowed to cross the phantom barrier $w(z)=-1$. We find that the additional freedom provided to $w(z)$ means the DE can undo changes in the background expansion induced by massive neutrinos at low redshifts. This has two significant consequences: (1) it leads to a substantial increase in the upper bound for the sum of the neutrino masses ($M_{\nu} < 0.33 - 0.55$ eV at the 95\% C.L. depending on the data sets and number of PCs included) compared to studies that choose a specific parametrization for $w(z)$; and (2) it causes $\sim1\sigma$ deviations from $\Lambda$CDM in the luminosity distance and the Hubble expansion rate at higher redshifts ($z \gtrsim 2$), where the contribution of DE is subdominant and there is little constraining data. The second point consequently means that there are also observable deviations in the shear power spectrum and in the matter power spectrum at low redshift, since the clustering of matter throughout cosmic time depends on the expansion rate. This provides a compelling case to pursue high-$z$ BAO and SN measurements as a way of disentangling the effects of neutrinos and dark energy. Finally, we find that the additional freedom given to the dark energy component has the effect of lowering $S_8$ with respect to $\Lambda$CDM.