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SUMMARY:Cosmological Polytopes and the Wavefunction of the Universe
DTSTART;VALUE=DATE-TIME:20171218T140000Z
DTEND;VALUE=DATE-TIME:20171218T150000Z
DTSTAMP;VALUE=DATE-TIME:20180124T094724Z
UID:indico-event-14512@cern.ch
DESCRIPTION:Description: In this talk we present a novel approach to
understanding cosmological observables\, such as the wavefunction of the
universe and the late-time correlators. The general questions we ask are:
Which features should these observables have to come from a consistent
unitary evolution in cosmological space-time? If someone hands them to
us\, how do we check that they are correct? Concretely\, we focus on the
wavefunction of the universe for a class toy models of scalars with time-
dependent coupling constants\, including conformally coupled scalars (with
non-conformal interactions) in FRW cosmologies as a special case. We
discuss novel representations for such an observable. Strikingly\, we
found a connection between the physics of cosmological time evolution and
the wavefunction of the universe\, and the mathematics of positive
geometries. The contribution of each Feynman diagram to the wavefunction
of the universe is associated with a certain universal rational integrand.
We show that this integrand can be identified with the canonical form of
a “cosmological polytope”. These polytopes have an intrinsic
definition making no reference to physics\, and the connection to
“time”\, along with familiar properties of the wavefunction\,
arises from this definition. In particular the singularity structure of
the wavefunction for this toy model of scalars is common to all
theories\, and is geometrized by the cosmological polytope. A natural
triangulation of the polytope is associated with the time-integral
representation of the wavefunction\; another natural triangulation of the
dual polytope reproduces “old-fashioned perturbation theory”. Other
triangulations are associated with efficient recursive computations of
the wavefunction\, while recently discovered new representations
for the canonical forms of general polytopes give new representations of
the wavefunction with no extant physical interpretation. We discuss in
some examples how symmetries of the cosmological polytope descend to
symmetries of the wavefunction\, (such as conformal invariance of deSitter
wavefunctions). Finally\, we will briefly comment how the flat-space
S-matrix is contained in this picture as a facet of the cosmological
polytope.\nURL: https://agenda.infn.it/conferenceDisplay.py?confId=14512
LOCATION:Dipartimento di Fisica e Astronomia Aula Teorici
URL:https://agenda.infn.it/conferenceDisplay.py?confId=14512
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