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We present a new, robust measurement of the evolving rest-frame UV galaxyluminosity function (LF) over the key redshift range z = 2 - 4. Our results arebased on the high dynamic range provided by combining the HUDF,CANDELS/GOODS-South, and UltraVISTA/COSMOS surveys. We utilise the unparalleledmulti-frequency photometry available in this survey `wedding cake' to compilecomplete galaxy samples at z ~ 2,3,4 via photometric redshifts (calibratedagainst the latest spectroscopy) rather than colour-colour selection, and todetermine accurate rest-frame UV absolute magnitudes from SED fitting. Our newdeterminations of the UV LF extend from M_{1500} ~ -22 down to M_{1500} =-14.5, -15.5 and -16 at z ~ 2, 3 and 4 respectively (thus reaching ~ 3 - 4magnitudes fainter than previous blank-field studies at z ~ 2 - 3). At z ~ 2 -3 we find a much shallower faint-end slope (alpha = -1.32 +- 0.03) than thesteeper values (alpha ~ -1.7) reported by Reddy & Steidel (2009) or by Alavi etal. (2014), and show that this new measurement is robust. By z ~ 4 thefaint-end slope has steepened slightly, to alpha = -1.43 +- 0.04, and we showthat these measurements are consistent with the overall evolutionary trend fromz = 0 to z = 8. Finally, we find that while characteristic number density(phi*) drops from z ~ 2 to z ~ 4, characteristic luminosity (M*) brightens by ~1 mag over this redshift range. This, combined with the new flatter faint-endslopes, has the consequence that UV luminosity density (and hence unobscuredstar-formation density) peaks at z ~ 2.5 - 3, when the Universe was ~ 2.5 Gyrold.

The galaxy UV luminosity function at z ~ 2 - 4; new results on faint-end slope and the evolution of luminosity density