Recently, the James Webb Space Telescope (JWST) Collaboration has found the unexpectedly large abundance of massive galaxies with stellar masses of $\sim {10}^{10}{M}_{\odot }$ at high redshifts $z\simeq 6.5–9$ compared with the prediction of the standard lambda cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) 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 ${\alpha }_s\simeq 0.02$ and ${\beta }_s\simeq 0.02$, a joint analysis with CMB observations shows that the tension can be resolved at the $1\sigma$ 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.

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• Inflation