Cosmological Polytopes and the Wavefunction of the Universe
By N. Arkani-Hamed, Paolo Benincasa, Alexander Postnikov. 2017
168 citations recorded by the source corpus.
We present a connection between the physics of cosmological time evolution and the mathematics of positive geometries, roughly analogous to similar connections seen in the context of scattering amplitudes. We consider the wavefunction of the universe in a class of toy models of conformally coupled scalars (with non-conformal interactions) in FRW cosmologies. The contribution of each Feynman diagram to the wavefunction of the universe is associated with a certain universal rational integrand, which we identify as the canonical form of a "cosmological polytope", which have an independent, intrinsic definition, making no reference to physics. The singularity structure of the wavefunction for this model of scalars is common to all theories, and is geometrized by the cosmological polytope. Natural triangulations of the polytope reproduce the path-integral and "old-fashioned perturbation theory" representations of the wavefunction, and we also find new representations of the wavefunction with no extant physical interpretation. We show in suitable examples how symmetries of the cosmological polytope descend to symmetries of the wavefunction, (such as conformal invariance). In cases such as $\phi^3$ theory in $dS_4$, the final wavefunction obtained from integration of the rational functions gives rise to polylogarithms associated with every graph. We give an explicit expression for the symbol of these polylogs, which record the geometry of sequential projections of the cosmological polytope.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e065f2202e42174bd570e85064bce6569e7c39ba
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Citations in the corpus
- The Cosmological Bootstrap: Spinning correlators from symmetries and factorization (2020, methodology): “This implies the following recursion relation [51]”
- The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “• Some very early steps in identifying new combinatoric/geometric structures underlying cosmological correlators, playing a roughly analogous role to amplituhedra and generalized associahedra for scattering amplitudes, have recently appeared in [134] with the discovery of “cosmological polytopes”, a”
- The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “Recently, a similar bootstrap philosophy was applied to cosmological correlation functions [1] (see also [2–7]).”
- Building a boostless bootstrap for the bispectrum (2020, methodology): “These singularities have been the focus of much recent interest in the literature [23, 25, 26, 14, 15, 19, 27].”