A search for the first galaxies across $>0.6$ deg$^2$ of JWST imaging: new evidence for a rapid decline in star-formation activity at $z>12$

We present a new determination of the evolving galaxy UV luminosity function (LF) over the extreme redshift range $12.5$0.6 deg$^2$ of JWST NIRCam imaging containing $>150$ independent sight-lines. We find evidence for an accelerated decline in the UV LF, and hence inferred star-formation rate density ($\rho_{\rm SFR}$), over the $\simeq100\rm{Myr}$ cosmic time interval between $z=11$ and $z=13.5$. Moreover, based on a notable lack of galaxy candidates at $z>14.5$, we find evidence for an even more rapid descent in star-formation activity towards earlier times, with our new measurement of $\rho_{\rm SFR}$ at $z\simeq15.5$ lying significantly below an extrapolation of the log-linear $\rho_{\rm SFR}(\rm z)$ relation inferred from early JWST LF studies. Instead, we find that the evolution in $\rho_{\rm SFR}(\rm z)$ at these very early times is better described by a piece-wise log-linear relation, in which the decline in $\rho_{\rm SFR} (\rm z)$ at $z>12$ is $\simeq4$ times steeper than at redshifts $z<12$. Our observational results are consistent with a number of theoretical models of galaxy evolution which have incorporated a range of treatments in an attempt to explain the prevalence of UV-bright galaxies at least out to $z \simeq 12$ (e.g., increased star-formation efficiency, stochastic star-formation histories, an evolving stellar initial mass function and/or a shift towards attenuation-free stellar populations). However, our results are also entirely consistent with a relatively simple galaxy evolution model with no such adjustments, in which the rapid evolution of the dark-matter halo mass function at early times is for a while partially masked by progressively younger stellar ages, with the inferred epoch of first galaxy formation lying at $z\simeq15$.