Linking the Singularities of Cosmological Correlators

Abstract

Much of the structure of cosmological correlators is controlled by their singularities, which in turn are fixed in terms of flat-space scattering amplitudes. An important challenge is to interpolate between the singular limits to determine the full correlators at arbitrary kinematics. This is particularly relevant because the singularities of correlators are not directly observable, but can only be accessed by analytic continuation. In this paper, we study rational correlators-including those of gauge fields, gravitons, and the inflaton-whose only singularities at tree level are poles and whose behavior away from these poles is strongly constrained by unitarity and locality. We describe how unitarity translates into a set of cutting rules that consistent correlators must satisfy, and explain how this can be used to bootstrap correlators given information about their singularities. We also derive recursion relations that allow the iterative construction of more complicated correlators from simpler building blocks. In flat space, all energy singularities are simple poles, so that the combination of unitarity constraints and recursion relations provides an efficient way to bootstrap the full correlators. In many cases, these flat-space correlators can then be transformed into their more complex de Sitter counterparts. As an example of this procedure, we derive the correlator associated to graviton Compton scattering in de Sitter space, though the methods are much more widely applicable.

Exceptional scalar theories in de Sitter space

“…This is the purview of the cosmological bootstrap, which aims to classify the space of possible cosmological correlators, and so constrain the physics of inflation (see, e.g., Refs. [54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] for recent developments). It is natural to wonder about the role of these scalar theories in the bootstrap construction: how precisely are their special properties reflected in their (A)dS correlators?…”

Cutting Rule for Cosmological Collider Signals: A Bulk Evolution Perspective

“…Finally, a comparison must be made between our method and the recently proposed cosmological cutting rules [47,48,50,51]. Based on general principles such as locality, unitarity and analyticity, the cosmological cutting rules give precise relations among the discontinuities of wavefunction exponents Disc k I ψ n .…”

“…Methods from the AdS toolkit, such as the Mellin-Barnes representation, are applied to tree-level processes with useful results [45,46]. The recent cutting rules utilize locality, unitarity and analyticity, to derive general recursion relations for the discontinuity of cosmological wavefunctions [47][48][49][50][51]. More formally, the cosmological polytopes provide an intriguing geometric picture for the CC process, while also hinting connections between cosmological correlators and flat spacetime scattering amplitudes [52].…”

Physical Representations for Scattering Amplitudes and the Wavefunction of the Universe

“…In cosmology, the understanding of relevant quantum mechanical observables, such as the spatial correlations and the wavefunction of the universe, as well as the physics they encode and the technology to compute them, are all significantly more primitive. The way that fundamental physical principles, such as unitarity and causality, reflect into and constrain these observables, started to be elucidated only recently, via the proof of a cosmological optical theorem [27] and the associated cutting rules [28][29][30][31], the positivity of the spectral den-sity [32,33], as well as the proof of existence Steinmannlike relations [34].…”