  Correlation functions of primordial density fluctuations provide an exciting
probe of the physics governing the earliest moments of our Universe. However,
the standard approach to compute them is technically challenging. Theoretical
predictions are therefore available only in restricted classes of theories. In
this Letter, we present a complete method to systematically compute tree-level
inflationary correlators. This method is based on following the time evolution
of equal-time correlators and it accurately captures all physical effects in
any theory. These theories are conveniently formulated at the level of
inflationary fluctuations, and can feature any number of degrees of freedom
with arbitrary dispersion relations and masses, coupled through any type of
time-dependent interactions. We demonstrate the power of this approach by
exploring the properties of the cosmological collider signal, a discovery
channel for new high-energy physics, in theories with strong mixing and in the
presence of features. This work lays the foundation for a universal program to
assist our theoretical understanding of inflationary physics and generate
theoretical data for an unbiased interpretation of upcoming cosmological
observations.
