Hints, neutrino bounds, and WDM constraints from SDSS DR14 Lyman-α and Planck full-survey data

The Ly-$\alpha$ forest 1D flux power spectrum is a powerful probe of several cosmological parameters. Assuming a $\Lambda$CDM cosmology including massive neutrinos, we find that the latest SDSS DR14 BOSS and eBOSS Ly-$\alpha$ forest data is in very good agreement with current weak lensing constraints on $(\Omega_m, \sigma_8)$ and has the same small level of tension with Planck. We did not identify a systematic effect in the data analysis that could explain this small tension, but we show that it can be reduced in extended cosmological models where the spectral index is not the same on the very different times and scales probed by CMB and Ly-$\alpha$ data. A particular case is that of a $\Lambda$CDM model including a running of the spectral index on top of massive neutrinos. With combined Ly-$\alpha$ and Planck data, we find a slight (3$\sigma$) preference for negative running, $\alpha_s= -0.010 \pm 0.004$ (68% CL). Neutrino mass bounds are found to be robust against different assumptions. In the $\Lambda$CDM model with running, we find $\sum m_\nu 10\;\mathrm{keV}$ (95% CL) from Ly-$\alpha$ data alone.