Kavli Affiliate: Austin Joyce

| First 5 Authors: Nima Arkani-Hamed, Daniel Baumann, Aaron Hillman, Austin Joyce, Hayden Lee

| Summary:

Cosmological fluctuations retain a memory of the physics that generated them

in their spatial correlations. The strength of correlations varies smoothly as

a function of external kinematics, which is encoded in differential equations

satisfied by cosmological correlation functions. In this work, we provide a

broader perspective on the origin and structure of these differential

equations. As a concrete example, we study conformally coupled scalar fields in

a power-law cosmology. The wavefunction coefficients in this model have

integral representations, with the integrands being the product of the

corresponding flat-space results and "twist factors" that depend on the

cosmological evolution. These integrals are part of a finite-dimensional basis

of master integrals, which satisfy a system of first-order differential

equations. We develop a formalism to derive these differential equations for

arbitrary tree graphs. The results can be represented in graphical form by

associating the singularities of the differential equations with a set of graph

tubings. Upon differentiation, these tubings grow in a local and predictive

fashion. In fact, a few remarkably simple rules allow us to predict — by hand

— the equations for all tree graphs. While the rules of this "kinematic flow"

are defined purely in terms of data on the boundary of the spacetime, they

reflect the physics of bulk time evolution. We also study the analogous

structures in ${rm tr},phi^3$ theory, and see some glimpses of hidden

structure in the sum over planar graphs. This suggests that there is an

autonomous combinatorial or geometric construction from which cosmological

correlations, and the associated spacetime, emerge.

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