Life beyond 30: probing the $-20

We present the ultraviolet luminosity function and an estimate of the cosmic star formation rate density at $88$ galaxy candidates based on their dropout nature in the $F115W$ and/or $F150W$ filters, a high probability for their photometric redshifts, estimated with three different codes, being at $z>8$, good fits based on $\chi^2$ calculations, and predominant solutions compared to $z<8$ alternatives. We find mild evolution in the luminosity function from $z\sim13$ to $z\sim8$, i.e., only a small increase in the average number density of $\sim$0.2~dex, while the faint-end slope and absolute magnitude of the knee remain approximately constant, with values $\alpha=-2.3\pm0.2$ and $M^*=-20.8\pm0.2$~mag. Comparing our results with the predictions of a wide range of state-of-the-art galaxy evolution models, we find two main results: (1) a slower increase with time in the cosmic star formation rate density compared to a steeper rise predicted by models; (2) nearly a factor of 10 higher star formation activity concentrated in scales around 2~kpc in galaxies with stellar masses $\sim10^8$~M$_\odot$ during the first 350~Myr of the Universe ($z\sim12$), with models matching better the observations $\sim$150~Myr later, by $z\sim9$.