  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 $\sim 90$ eV. The new DESI survey, coupled with high-accuracy
modeling, will help distinguish the source of this discrepancy.
