EPOCHS Paper II: The Ultraviolet Luminosity Function from $7.5<z<13.5$ using 180 square arcminutes of deep, blank-fields from the PEARLS Survey and Public JWST data

We present an analysis of the ultraviolet luminosity function (UV LF) and star formation rate density of distant galaxies ($7.5 < z < 13.5$) in the `blank' fields of the Prime Extragalactic Areas for Reionization Science (PEARLS) survey combined with Early Release Science (ERS) data from the CEERS, GLASS, NGDEEP surveys/fields and the first data release of JADES. We use strict quality cuts on EAZY photometric redshifts to obtain a reliable selection and characterisation of high-redshift ($z>6.5$) galaxies from a consistently processed set of deep, near-infrared imaging. Within an area of 180 arcmin$^{2}$, we identify 1046 candidate galaxies at redshifts $z>6.5$ and we use this sample to study the ultraviolet luminosity function (UV LF) in four redshift bins between $7.5<z<13.5$. The measured number density of galaxies at $z=8$ and $z=9$ match those of past observations undertaken by the {\em Hubble Space Telescope} (HST). Our $z=10.5$ measurements lie between early JWST results and past HST results, indicating cosmic variance may be the cause of previous high density measurements. However, number densities of UV luminous galaxies at $z=12.5$ are high compared to predictions from simulations. When examining the star formation rate density of galaxies at this time period, our observations are still largely consistent with a constant star formation efficiency, are slightly lower than previous early estimations using JWST and support galaxy driven reionization at $z\leq8$.