$5 \sigma$ tension between Planck cosmic microwave background and eBOSS Lyman-alpha forest and constraints on physics beyond $\Lambda$CDM

We find that combined Planck cosmic microwave background, baryon acoustic oscillations and supernovae data analyzed under $\Lambda$CDM are in 4.9$\sigma$ tension with eBOSS Ly$\alpha$ forest in inference of the linear matter power spectrum at wavenumber $\sim 1 h\,\mathrm{Mpc}^{-1}$ and redshift = 3. Model extensions can alleviate this tension: running in the tilt of the primordial power spectrum ($\alpha_\mathrm{s} \sim -0.01$); a fraction $\sim (1 - 5)\%$ of ultra-light axion dark matter (DM) with particle mass $\sim 10^{-25}$ eV or warm DM with mass $\sim 10$ eV. The new DESI survey, coupled with high-accuracy modeling, will help distinguish the source of this discrepancy.