Early universe cosmology is entering a new phase thanks to more precise measurements constraining the primordial density inhomogeneities. Current and near future large scale structure surveys are pursuing statistics of the inhomogeneities beyond the well-measured power spectrum, and will eventually improve on the recent results from the Planck satellite. The potential of these new statistics has changed the way we think about theories of the primordial universe, including inflation. I will present the current understanding of how new data may illuminate the particle physics of inflation. I will also present new results, motivated by possible signatures of primordial physics in the halo bias, on an old issue in inflation: our ability to test the theory is limited by the fact that we observe a single, finite universe.
