The PAU Survey: the i-band galaxy luminosity function from the present-day to z = 2

We present a measurement of the i-band galaxy luminosity function from the present-day to z = 2, using over 1.1 million galaxies from the Physics of the Accelerating Universe Survey (PAUS). PAUS combines broad-band imaging from the Canada–France–Hawaii Telescope Lensing Survey with narrow-band photometry from PAUCam, enabling high-precision photometric redshifts with an accuracy of σ₆₈(z) = 0.019 down to i_AB = 23. A synthetic light-cone mock catalogue built using the galform semi-analytic model is used to simulate PAUS selection effects and photometric uncertainties, and to derive a machine-learning based estimate of the k-correction. We recover rest frame i-band luminosities using a random forestregressortrained on simulated ugriz photometry and redshifts. Luminosity functions are estimated using the 1/V_max method, accounting for photometric redshift and magnitude errors, and validated against mock data. We find good agreement between observations and models at z < 1, with increasing discrepancies at higherredshifts due to photometric redshift outliers. The bright-end of the luminosity function becomes flatter at high redshift, primarily driven by redshift errors. We show that the faint-end of the luminosity function becomes more incomplete with increasing redshift, but isstill useful for constraining models. We analyse the red and blue galaxy populations separately, observing distinct evolutionary trends. The model overpredicts the number of both faint red and blue galaxies. Our study highlights the importance of accurate redshift estimation and selection modelling for robust luminosity function recovery, and demonstratesthat PAUS can characterize the galaxy population with photometric redshifts across a wide redshift baseline.