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Résumé |
Our understanding of physical phenomena is intimately linked
to the way we understand the relevant observables describing them. While
a big deal of progress has been made for processes occurring in flat
space-time, much less is known in cosmological settings. In this
context, we have processes which happened in the past and which we can
detect the remnants of at present time. Thus, the relevant observable is
the late-time wavefunction of the universe. Questions such as "what
properties they ought to satisfy in order to come from a consistent time
evolution in cosmological space-times?", are still unanswered, and are
compelling given that in these quantities time is effectively integrated
out. In this talk I will report on some recent progress in this
direction, aiming towards the idea of a formulation of cosmology
"without time". Amazingly enough, a new mathematical structure, we
called "cosmological polytope", which has its own first principle
definition, encodes the singularity structure we ascribe to the
perturbative wavefunction of the universe, and makes explicit its
(surprising) relation to the flat-space S-matrix. I will stress how the
cosmological polytopes allow us to: compute the wavefunction of the
universe at arbitrary points and arbitrary loops (with novel
representations for it); interpret the residues of its poles in terms of
flat-space processes; provide a general geometrical proof for the
flat-space cutting rules; reconstruct the perturbative wavefunction from
the knowledge of the flat-space S-matrix and a subset of symmetries
enjoyed by the wavefunction. |
