We study the faint radio population using wide-field very long baseline interferometry (VLBI) observations of 2865 known radio sources in the Cosmic Evolution Survey (COSMOS) field. The main objective of the project was to determine where active galactic nuclei (AGN) are present. The combination of number of sources, sensitivity, angular resolution and area covered by this project are unprecedented. We have detected 468 radio sources, expected to be AGNs, with the Very Long Baseline Array (VLBA) at 1.4 GHz. This is, to date, the largest sample assembled of VLBI detected sources in the sub-mJy regime. The input sample was taken from previous observations with the Very Large Array (VLA). We present the catalogue with additional multiwavelength information. We find a detection fraction of 20%, considering only those sources from the input catalogue which were in principle detectable with the VLBA (2361). As a function of redshift, we see no evolution of the detection fraction over the redshift range 0.5<z<3. In addition, we find that faint radio sources typically have a greater fraction of their radio luminosity in a compact core: ~70% of the sub-mJy sources detected with the VLBA have more than half of their total radio luminosity in a VLBI-scale component, whereas this is true for only ~30% of the sources that are brighter than 10 mJy. This suggests that fainter radio sources differ intrinsically from brighter ones. Across our entire sample, we find the predominant morphological classification of the host galaxies of the VLBA detected sources to be early type (57%), although this varies with redshift and at z>1.5 we find that spiral galaxies become the most prevalent (48%). We demonstrate that wide-field VLBI observations, together with new calibration methods such as multi-source self-calibration and mosaicing, result in information which is difficult or impossible to obtain otherwise.
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