Cutting rule for cosmological collider signals: a bulk evolution perspective

Abstract

We show that the evolution of interacting massive particles in the de Sitter bulk can be understood at leading order as a series of resonant decay and production events. From this perspective, we classify the cosmological collider signals into local and nonlocal categories with drastically different physical origins. This further allows us to derive a cutting rule for efficiently extracting these cosmological collider signals in an analytical fashion. Our cutting rule is a practical way for extracting cosmological collider signals in model building, and can be readily implemented as symbolic computational packages in the future.

Phase Information in Cosmological Collider Signals

“…However, the separation of the 4-point function into three parts (6) still applies when we move away from the squeezed limit. In the general situation, it is known that the signal is contributed by the symmetric part of the propagator, namely the part invariant under the exchange τ 1 ↔ τ 2 [62]. Due to this exchange symmetry, the time ordering in the Schwinger-Keldysh diagrammatic calculation becomes irrelevant, and one can finish the time integral of each interaction vertex sepaprately.…”

“…Meanwhile, theoretical understanding of inflationary correlation functions has been advanced with multiple approaches, including the cosmological bootstrap program [46][47][48][49][50][51][52], the AdS-inspired Mellin space approach [53][54][55][56], and a direct numerical approach [57]. Results have also been obtained on the analytical structure of cosmic correlators [58][59][60][61][62]. See also [63][64][65].…”

Large Spin-2 Signals at the Cosmological Collider

“…Our strategy is to apply the recently developed cutting rule [31] (see a brief review in Appendix B) to obtain analytical results of the leading-order CC signals. They are then checked against the results from direct numerical integration.…”

“…Based on this observation, one can approximate any tree diagrams by a combination of CC signals and EFT backgrounds. We briefly summarize the general algorithm below, and refer interested readers to [31] for more details.…”

“…It has been shown that one of the most salient feature of the corresponding CC signal in the curvature bispectrum is a characteristic P 2 (cos θ) angular dependence [21,22,30], due to the mixing between the longitudinal component of the spinning particle and the inflaton. However, the overall amplitude of the CC signal is exponentially suppressed by the particle mass m. This is because the non-local type CC signal comes from on-shell particle production [31]. But a pure gravitational production is subjected to a Boltzmann suppression e −m/T dS with the intrinsic de Sitter (dS) temperature T dS = H 2π .…”