ABSTRACT We present a new determination of the evolving galaxy ultraviolet (UV) luminosity function (LF) over the redshift range $8.5< z< 15.5$ using a combination of several major Cycle-1 JWST imaging programmes – Public Release IMaging for Extragalactic Research, JWST Advanced Deep Extragalactic Survey, and Next Generation Deep Extragalactic Exploratory Public Survey. This multifield approach yields a total of $\simeq 370$ arcmin2 of JWST/NIRCam imaging, reaching (5-$\sigma$) depths of $\simeq 30$ AB mag in the deepest regions. We select a sample of 2548 galaxies with a significant probability of lying at high redshift ($p(z> 8.5)> 0.05$) to undertake a statistical calculation of the UV LF. Our new measurements span $\simeq 4$ mag in UV luminosity at $z=9-12.5$, placing new constraints on both the shape and evolution of the LF at early times. Our measurements yield a new estimate of the early evolution of cosmic star-formation rate density ($\rho _{\rm {SFR}}$) confirming the gradual decline deduced from early JWST studies, at least out to $z \simeq 12$. Finally we show that the observed early evolution of the galaxy UV LF (and $\rho _{\rm {SFR}}$) can be reproduced in a ${\rm \Lambda }$cold dark matter Universe, with no change in dust properties or star-formation efficiency required out to $z \simeq 12$. Instead, a progressive trend towards younger stellar population ages can reproduce the observations, and the typical ages required at $z \simeq$ 8, 9, 10, and 11 all converge on $\simeq 380-330$ Myr after the big bang, indicative of a rapid emergence of early galaxies at $z \simeq 12 - 13$. This is consistent with the first indications of a steeper drop-off in $\rho _{\rm {SFR}}$ we find beyond $z \simeq 13$, possibly reflecting the rapid evolution of the halo mass function at earlier times.
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