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

We find that combined Planck cosmic microwave background, baryon acoustic oscillations and supernovae data analyzed under $\mathrm{\Lambda }$CDM are in 4.9$\sigma$ tension with eBOSS Ly$\alpha$ forest in inference of the linear matter power spectrum at wavenumber $\sim 1h{\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$ 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 $\sim (1-5)\mathrm{\%}$ 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.