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 $\Lambda$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 $\alpha_s \simeq 0.2$ and $\beta_s \simeq 0.2$, 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.