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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