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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