Alleviating the need for exponential evolution of JWST galaxies in 10${}^{10}{M}_{\odot }$ haloes at $z>10$ by a modified $\mathrm{\Lambda }$CDM power spectrum

We infer the evolution of the UV luminosities of galaxies in haloes of masses ${10}^{10}-{10}^{11}{M}_{\odot }$ in the redshift range of $z\sim 9-16$ from the recent JWST data. Within the standard $\mathrm{\Lambda }$CDM cosmological model, it is found that the average luminosities in this halo mass range show an exponential evolution with redshift, in excess of that expected from astrophysical considerations including the evolution of UV luminosity from Population III galaxies. We find that an enhancement of power on scales $k\sim 1$ Mpc${}^{-1}$, as captured by a cosmological transfer function modified from the $\mathrm{\Lambda }$CDM form, is able to alleviate this effect and allow for a non-evolving UV luminosity as a function of redshift at $z>10$, consistently with the corresponding findings for lower redshifts. We discuss the possible astrophysical and cosmological reasons for such an enhancement.