Boostless Cosmological Collider Bootstrap

TL;DR

This work develops a boostless cosmological bootstrap to classify inflationary three-point functions with boost-breaking interactions, producing a complete set of single-exchange bispectra for both scalar and spinning exchanges. A central achievement is the scalar seed construction from a mixed propagator between the inflaton and a massive field, governed by the boundary differential equation $\Delta_u\,\hat{\mathcal{I}}(u)$ with $\mu=\sqrt{m^2/H^2-9/4}$, whose solution is decomposed into homogeneous and particular parts and extended to generalized seeds for various sound speeds $c_s$. Using boost-breaking weight-shifting and spin-raising operators, these seeds bootstrap into analytic inflationary bispectra for massless external fields, revealing new phenomenology such as phase-shifted oscillations in the squeezed limit and equilateral-configuration oscillations when the mediator has a low sound speed. The results provide a physically motivated, largely non-slow-roll framework with potentially large non-Gaussian signals, offering templates for near-future cosmological surveys and a richer landscape of collider-like signatures beyond de Sitter symmetry. Overall, the paper delivers an explicit, analytic catalogue of boostless collider shapes for scalar and higher-spin exchanges, grounded in boundary differential equations and operator methods.

Abstract

Cosmological correlation functions contain valuable information about the primordial Universe, with possible signatures of new massive particles at very high energies. Recent developments, including the cosmological bootstrap, bring new perspectives and powerful tools to study these observables. In this paper, we systematically classify inflationary three-point correlators of scalar perturbations using the bootstrap method. For the first time, we derive a complete set of single-exchange cosmological collider bispectra with new shapes and potentially detectable signals. Specifically, we focus on the primordial scalar bispectra generated from the exchange of massive particles with all possible boost-breaking interactions during inflation. We introduce three-point "seed" functions, from which we bootstrap the inflationary bispectra of scalar and spinning exchanges using weight-shifting and spin-raising operators. The computation of the seed function requires solving an ordinary differential equation in comoving momenta, a boundary version of the equation of motion satisfied by a propagator that linearly mixes a massive particle with the external light scalars. The resulting correlators are presented in analytic form, for any kinematics. These shapes are of interest for near-future cosmological surveys, as the primordial non-Gaussianity in boost-breaking theories can be large. We also identify new features in these shapes, which are phenomenologically distinct from the de Sitter invariant cases. For example, the oscillatory shapes around the squeezed limit have different phases. Furthermore, when the massive particle has much lower speed of sound than the inflaton, oscillatory features appear around the equilateral configuration.

Figures (2)

• Figure 1: The structure of this paper. We compute the bispectrum of conformally coupled scalars with a massless scalar that linearly mixes with a massive scalar field. From this building block, and various "weight-shifting" and "spin-raising" operations, we generate a wide variety of inflationary bispectra of phenomenological interest. As we relax the requirement of boost symmetry, the signals can be large enough to be detectable in near-future cosmological surveys. The procedure to obtain the scalar seed, as well as the various weight-shifting moves, are presented in the sections indicated above.
• Figure 2: A diagrammatic illustration of how large boost-breaking interactions arise for the exchange bispectrum. In Feynman diagrams of cosmological correlators, the breaking of the boost symmetry is normally associated with evaluating external legs of the massless scalar to the background (the dashed lines with $\dot\Phi$). The (boostless) EFT diagram on the left encompasses all the higher-derivative contributions on the right-hand side systematically.