We have overwhelming evidence that the distribution of everything on very large scales is of primorial origin. According to the leading paradigm of inflation, the statistics of these primordial perturbations can be traced back to correlators of quantum fields on a curved quasi-de Sitter spacetime. This gives us the unique opportunity to probe the fundamental laws of physics at very high energies as well as the perturbative regime of quantum gravity.
Unfortunately, due to the creativity of theorists and the paucity of data about the primordial universe, there is a huge number of models compatible with all measurements, featuring a wide variety of mechanisms, symmetries, and spectra of particles. The reason can be traced back to the fact that we don't observe the time evolution during inflation, but only its final outcome.
In this talk I will report on the recent progress in developing a completely new "bootstrap" approach to derive predictions from the very early universe that make no reference to time and the un-observable time evolution. The bootstrap approach builds directly upon the fundamental pillars of physics, namely unitarity, locality and symmetries and is highly model independent. I will show how these principles can be used to derive many classical and new inflationary predictions associated with primordial non-Gaussianity in a way that is both computationally simpler and conceptually more transparent.