TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.6.157
TI  - Perturbative unitarity and the wavefunction of the Universe
PY  - 2024/06/20
UR  - https://scipost.org/SciPostPhys.16.6.157
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 6
SP  - 157
A1  - Albayrak, Soner
AU  - Benincasa, Paolo
AU  - Duaso Pueyo, Carlos
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.6.157,
	title={{Perturbative unitarity and the wavefunction of the Universe}},
	author={Soner Albayrak and Paolo Benincasa and Carlos Duaso Pueyo},
	journal={SciPost Phys.},
	volume={16},
	pages={157},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.6.157},
	url={https://scipost.org/10.21468/SciPostPhys.16.6.157},
}