Kavli Affiliate: Austin Joyce
| First 5 Authors: Daniel Baumann, Harry Goodhew, Austin Joyce, Hayden Lee, Guilherme L. Pimentel
| Summary:
We uncover a geometric organization of the differential equations for the
wavefunction coefficients of conformally coupled scalars in power-law
cosmologies. To do this, we introduce a basis of functions inspired by a
decomposition of the wavefunction into time-ordered components. Representing
these basis functions and their singularities by graph tubings, we show that a
remarkably simple rule for the merger of tubes produces the differential
equations for arbitrary tree graphs (and loop integrands). We find that the
basis functions can be assigned to the vertices, edges, and facets of convex
geometries (in the simplest cases, collections of hypercubes) which capture the
compatibility of mergers and define how the basis functions are coupled in the
differential equations. This organization of functions also simplifies solving
the differential equations. The merger of tubes is shown to reflect the causal
properties of bulk physics, in particular the collapse of time-ordered
propagators. Taken together, these observations demystify the origin of the
kinematic flow observed in these equations [1].
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