With the 2015 results from the PLANCK satellite, the cosmic microwave background (CMB) temperature anisotropies has reached its cosmic variance limit.
Future progress in Cosmology therefore lies in late time measurements, and on smaller scales, going beyond linear theory.
I will start by discussing the status of inflation in light of these results, and point on some (classes) of models that are in accord with observations, as well as consequences for String theory model building.
Then I will discuss ideas on going beyond linear theory. From the observational standpoint, I will report on progress in using Supernovae lensing as a cosmological probe.
If time permits, I will discuss some theoretical progress in consistency relations for large scale structure.