An inflation model for massive primordial black holes to interpret the JWST observations

The first observations of the James Webb Space Telescope (JWST) have identified six massive galaxy candidates with the stellar masses $M_\ast\gtrsim 10^{10}\,M_\odot$ at high redshifts $7.4\lesssim z\lesssim 9.1$, with two most massive high-$z$ objects having the cumulative comoving number densities $n_{\rm G}$ up to $1.6\times 10^{-5}\, {\rm Mpc}^{-3}$. The presence of such massive sources in the early universe challenges the standard $\Lambda$CDM model since the needed star formation efficiency is unrealistically high. This tension can be alleviated via the accretion of massive primordial black holes (PBHs). In this work, with the updated data from the first JWST observations, we find that the PBHs with mass $10^8\,M_\odot\lesssim M_{\rm PBH}\lesssim 10^{11}\,M_\odot$ can act as the seeds of extremely massive galaxies even with a low abundance $10^{-7}\lesssim f_{\rm PBH}\lesssim 10^{-3}$. We construct an ultraslow-roll inflation model and investigate its possibility of producing the required PBHs. We explore the model in two cases, depending on whether there is a perfect plateau on the inflaton potential. If the plateau is allowed to incline slightly, our model can produce the PBHs that cover the required PBH mass and abundance range to explain the JWST data.