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

International audienceThe Lyman-α forest 1D flux power spectrum is a powerful probe of several cosmological parameters. Assuming a ΛCDM cosmology including massive neutrinos, we find that the latest SDSS DR14 BOSS and eBOSS Lyman-α forest data is in very good agreement with current weak lensing constraints on (Ωm, σ8) 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 Lyman-α data. A particular case is that of a ΛCDM model including a running of the spectral index on top of massive neutrinos. With combined Lyman-α and Planck data, we find a slight (3σ) preference for negative running, αs= −0.010 ± 0.004 (68%CL). Neutrino mass bounds are found to be robust against different assumptions. In the ΛCDM model with running, we find ∑ mν 5.3 keV (95%CL)