Lessons on early structure formation from a mature galaxy cluster observed at cosmic noon

We demonstrate a new approach of indirectly constraining both early star and structure formation via mature galaxy clusters at cosmic noon (z similar to 2), using the cluster XLSSC 122 as an example. With the standard Press Schechter formalism, we infer a rapid evolution of the star formation efficiency (the ratio of stellar to halo mass) from 10(-4) to 0.01 during z similar to 20-13, based on the age distribution of stars in post-starburst galaxies of XLSSC 122, measured by Hubble Space Telescope photometry assuming no dust extinction. Here, we consider all low-mass haloes, including minihaloes, that host the first stars and galaxies 5 x 10(5) M-circle dot less than or similar to M-halo less than or similar to 10(10) M-circle dot). We also place new constraints on fuzzy dark matter models of m(a) less than or similar to 5 x 10(-21) eV/c(2) for the ultralight boson mass, from the abundance of galaxies with star formation at z greater than or similar to 13 in XLSSC 122. Our exploratory results are consistent with existing constraints. More comprehensive results will be obtained if our approach is extended to a large sample of clusters or field post-starburst galaxies at cosmic noon, with improved modelling of halo and stellar populations.