| Abstract
| - Context. The size of a galaxy encapsulates the signature of the different physical processes driving its evolution. The distribution of galaxy sizes in the Universe as a function of cosmic time is therefore a key to understand galaxy evolution. Aims. We aim to measure the average sizes and size distributions of galaxies as they are assembling before the peak in the comoving star formation rate density of the Universe to better understand the evolution of galaxies across cosmic time. Methods. We used a sample of ~1200 galaxies in the COSMOS and ECDFS fields with confirmed spectroscopic redshifts 2 ≤ zspec ≤ 4.5 in the VIMOS Ultra Deep Survey (VUDS), representative of star-forming galaxies with iAB ≤ 25 . We first derived galaxy sizes by applying a classical parametric profile-fitting method using GALFIT. We then measured the total pixel area covered by a galaxy above a given surface brightness threshold, which overcomes the difficulty of measuring sizes of galaxies with irregular shapes. We then compared the results obtained for the equivalent circularized radius enclosing 100% of the measured galaxy light r 100T ~2.2 to those obtained with the effective radius re,circ measured with GALFIT. Results. We find that the sizes of galaxies computed with our non-parametric approach span a wide range but remain roughly constant on average with a median value r 100T ~2.2 kpc for galaxies with 2 < z< 4.5 . This is in stark contrast with the strong downward evolution of re with increasing redshift, down to sizes of <1 kpc at z ~ 4.5 . We analyze the difference and find that parametric fitting of complex, asymmetric, multicomponent galaxies is severely underestimating their sizes. By comparing r 100T with physical parameters obtained through fitting the spectral energy distribution we find that the star-forming galaxies that are the largest at any redshift are, on average, more massive and form more stars. We discover that galaxies present more concentrated light profiles with increasing redshifts. We interpret these results as the signature of several, possibly different, evolutionary paths of galaxies in their early stages of assembly, including major and minor merging or star formation in multiple bright regions.
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