The network of tests shows the LCDM cosmology is a good approximation to what actually happened, but that need not mean it has all the physics relevant to cosmology back to light element formation. I will review properties of galaxies that seem to be particularly difficult to understand within LCDM and might be pointing to still better physics.
Constraining primordial non-Gaussianity can offer a window into the early universe, and into testing the inflationary paradigm, which is fully complementary to the approach offered by Cosmic Microwave Background polarization.
Large-scale structure and galaxy surveys have recently received renewed attention as a way to constrain primordial non-Gaussianity. I will review the potential and the limitations of this approach and highlight its complementarity to Cosmic Microwave Background observations.