HerMES: deep number counts at 250 μm, 350 μm and 500 μm in the COSMOS and GOODS-N fields and the build-up of the cosmic infrared background

Aims. The Spectral and Photometric Imaging REceiver (SPIRE) onboard the Herschel space telescope has provided confusion limited maps of deep fields at 250 μm, 350 μm, and 500 μm, as part of the Herschel Multi-tiered Extragalactic Survey (HerMES). Unfortunately, due to confusion, only a small fraction of the cosmic infrared background (CIB) can be resolved into individually-detected sources. Our goal is to produce deep galaxy number counts and redshift distributions below the confusion limit at SPIRE wavelengths (~20 mJy), which we then use to place strong constraints on the origins of the cosmic infrared background and on models of galaxy evolution. Methods. We individually extracted the bright SPIRE sources (>20 mJy) in the COSMOS field with a method using the positions, the flux densities, and the redshifts of the 24 μm sources as a prior, and derived the number counts and redshift distributions of the bright SPIRE sources. For fainter SPIRE sources (