Sadra Jazayeri, Xi Tong, Yuhang Zhu
A bstract Motivated by cosmological observations, we push the cosmological bootstrap program beyond the de Sitter invariance lamppost by considering correlators that explicitly break scale invariance, thereby exhibiting primordial features . For exchange processes involving heavy fields with time-dependent masses and sound speeds, we demonstrate that locality in the bulk implies a set of integro-differential equations for correlators on the boundary. These scale-breaking boundary equations come with a built-in memory kernel in momentum-kinematic space encapsulating the universe’s evolution during inflation. Specialising to heavy fields with sinusoidal masses such as those found in axion monodromy scenarios, we show that a powerful synthesis of microcausality and analyticity allows an analytical solution of these equations at leading order in the amplitude of mass oscillations. Meanwhile, we also unveil non-perturbative information in the integro-differential equations by resumming apparent infrared divergences as parametric resonances. In addition, we provide a first-of-its-kind example of numerical bootstrap that directly maps out the solution space of such boundary equations. Finally, we compute the bispectrum and uncover, in the squeezed limit, a scale-breaking cosmological collider signal, whose amplitude can be exponentially enhanced (with respect to the Boltzmann suppression) due to particle production triggered by high-frequency mass oscillations.