Blue-tilted spectral running and the JWST early galaxy tension

Recently, the James Webb Space Telescope (JWST) Collaboration has found the unexpectedly large abundance of massive galaxies with stellar masses of $\ensuremath{\sim}{10}^{10}{M}_{\ensuremath{\bigodot}}$ at high redshifts $z\ensuremath{\simeq}6.5--9$ compared with the prediction of the standard lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model. As a possible solution to the tension, we consider a blue-tilted spectrum of density perturbations with a positive running. We find that, for ${\ensuremath{\alpha}}_{s}\ensuremath{\simeq}0.02$ and ${\ensuremath{\beta}}_{s}\ensuremath{\simeq}0.02$, a joint analysis with CMB observations shows that the tension can be resolved at the $1\ensuremath{\sigma}$ confidence level. Such a blue-tilted spectrum is also plausible from the perspective for formations of primordial black holes on much smaller scales in the early Universe.