The cosmological flow: a systematic approach to primordial correlators

The time evolution of primordial fluctuations conceals a wealth of insights into the high-energy physics at play during the earliest moments of our Universe, which is ultimately encoded in late-time spatial correlation functions. However, the conventional procedure to compute them is technically challenging, and a complete dictionary mapping the landscape of inflationary theories and the corresponding observable signatures is not yet available. In this paper, we develop a framework to compute tree-level cosmological correlators based on following their time evolution from their origin as quantum zero-point fluctuations to the end of inflation. From first principles, the structure of the bulk time evolution imposes a set of universal differential equations in time satisfied by equal-time correlators. We automatise the process of systematically solving these equations. This allows us to accurately capture all physical effects and obtain exact results in theories formulated at the level of inflationary fluctuations that include any number of degrees of freedom with arbitrary dispersion relations and masses, coupled through any time-dependent interactions. We then illustrate the power of this formalism by exploring the phenomenology of cosmological correlators emerging from the interaction with a massive scalar field. After an extensive analysis of the quadratic theory and classifying perturbativity bounds, we study both the size and the shape dependence of non-Gaussianities in the entire parameter space, including the strong mixing regime. We present novel characteristics of cosmological collider signals in (would be) single-, double-, and triple-exchange three-point correlators. In the presence of primordial features, after subtracting gauge artefacts unavoidably generated by a breaking of scale-invariance, we show that soft limits of cosmological correlators offer a new possibility to probe the inflationary landscape. Finally, we provide templates to search for in future cosmological surveys.