Perturbative unitarity and the wavefunction of the Universe
Soner Albayrak, Paolo Benincasa, Carlos Duaso Pueyo
SciPost Phys. 16, 157 (2024) · published 20 June 2024
- doi: 10.21468/SciPostPhys.16.6.157
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Abstract
Unitarity of time evolution is one of the basic principles constraining physical processes. Its consequences in the perturbative Bunch-Davies wavefunction in cosmology have been formulated in terms of the cosmological optical theorem. In this paper, we re-analyse perturbative unitarity for the Bunch-Davies wavefunction, focusing on: $i)$ the role of the $i\epsilon$-prescription and its compatibility with the requirement of unitarity; $ii)$ the origin of the different ``cutting rules''; $iii)$ the emergence of the flat-space optical theorem from the cosmological one. We take the combinatorial point of view of the cosmological polytopes, which provide a first-principle description for a large class of scalar graphs contributing to the wavefunctional. The requirement of the positivity of the geometry together with the preservation of its orientation determine the $i\epsilon$-prescription. In kinematic space it translates into giving a small negative imaginary part to all the energies, making the wavefunction coefficients well-defined for any value of their real part along the real axis. Unitarity is instead encoded into a non-convex part of the cosmological polytope, which we name \textit{optical polytope}. The cosmological optical theorem emerges as the equivalence between a specific polytope subdivision of the optical polytope and its triangulations, each of which provides different cutting rules. The flat-space optical theorem instead emerges from the non-convexity of the optical polytope. On the more mathematical side, we provide two definitions of this non-convex geometry, none of them based on the idea of the non-convex geometry as a union of convex ones.
Cited by 8
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 2 Soner Albayrak,
- 3 Paolo Benincasa,
- 1 4 Carlos Duaso Pueyo
- 1 Institute of Physics, University of Amsterdam [IoP, UvA]
- 2 National Taiwan University [NTU]
- 3 Max-Planck-Institut für Physik / Max Planck Institute for Physics [MPP]
- 4 University of Cambridge