The Massive Flat Space Limit of Cosmological Correlators

Abstract: Identifying useful flat-space limits for cosmological correlators, where they can be expressed in terms of observables in Minkowski space is nontrivial due to their scale-invariant nature. In recent years, it has been shown that momentum-space correlators encode flat-space amplitudes at specific singularities that emerge in the complex plane of their kinematics after analytical continuation. This flat-space limit is massless in the sense that the amplitude corresponds to the ultraviolet regime of the associated flat-space process, where the masses of the internal propagators are effectively zero. In this paper, we introduce a novel massive flat-space (MFS) limit, in which the internal masses in the corresponding flat-space Feynman graph remain finite. Our proposal applies to arbitrary graphs with light external legs and heavy internal lines, using a double-scaling limit. In this limit, the external energies, treated as independent variables, approach zero in inverse proportion to the propagator masses, which are sent to infinity. We present a general reduction formula that expresses diagrams in this limit in terms of amputated Feynman graphs in flat space. Our findings underscore the deep connections between the rich structure of massive Feynman integrals and the properties of cosmological correlators involving the exchange of heavy fields. Using this reduction formula, we compute sample one-loop contributions from heavy particles to inflationary correlators in the small sound-speed regime, revealing novel bispectrum shapes. The non-Gaussian signals we uncover, which are especially pronounced around the equilateral configuration, cannot be reproduced by adding local terms to the effective field theory of single-field inflation. Instead, they are captured by incorporating prescribed spatially non-local operators into the EFT.