Blue-tilted Runnings and the JWST Early Galaxy Tension

The recent James Webb Space Telescope (JWST) observations reported 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 $\mathrm{\Lambda }$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 of primordial black hole formation on much smaller scales in the early Universe.