Probing fundamental physics with the evolved Universe

The talk will discuss how the observed structure in the evolved (last 1 Gyr) Universe offers a unique probe of fundamental physical theories operating on cosmological scales. The focus will be on implications of deviations of motions of galaxies from a pure Hubble flow of the cosmic background. While the standard cosmological model with a cosmological constant term and Cold Dark Matter (LCDM) is highly successful in reproducing most features several peculiarities persist. I will present generic predictions and features of modified models that overcome the remiaining mismatches of LCDM.