Dispersive Bootstrap of Massive Inflation Correlators

Abstract: Inflation correlators with massive exchanges are central observables of cosmological collider physics, and are also important theoretical data for us to better understand quantum field theories in dS. However, they are difficult to compute directly due to many technical complications of the Schwinger-Keldysh integral. In this work, we initiate a new bootstrap program for massive inflation correlators with dispersion relations on complex momentum planes. We classify kinematic variables of a correlator into vertex energies and line energies, and develop two distinct types of dispersion relations for both of them, respectively called vertex dispersion and line dispersion relations. These dispersion methods allow us to obtain full analytical results of massive correlators from a knowledge of their oscillatory signals alone, while the oscillatory signal at the tree level can be related to simpler subgraphs via the cutting rule. We further apply this method to massive loop correlators, and obtain new analytical expressions for loop diagrams much simpler than existing results from spectral decomposition. In particular, we show that the analyticity demands the existence of an "irreducible background" in the loop correlator, which is unambiguously defined, free of UV divergence, and independent of renormalization schemes.