One of the biggest questions in all of science is the origin of structure in the Universe. What created
everything that we see around us? There are hints suggesting that the answer involves a fascinating
connection between the physics of the very small and the very large.
We have learned that our Universe evolved from a hot and dense state, the hot Big Bang. The observed
distribution of galaxies on the sky provides a window on the history of the Universe. These observations can
be traced back to patterns in the density variations at the origin of the hot Big Bang, which are called
primordial fluctuations. .
Recent cosmological observations have revealed the remarkable fact that these primordial fluctuations must
have been created before the hot Big Bang. The conventional Big Bang was therefore not the beginning of
time, but rather the end of an earlier high-energy period, and the primordial fluctuations were created in this
pre-Big Bang phase. But, how exactly did this happen? The leading proposal is that the early universe
experienced a phase of very rapid expansion known as inflation. During this inflationary period, small
quantum fluctuations were stretched to cosmic scales and became the density fluctuations which seeded the
formation of stars and galaxies. Although this provides an elegant explanation for the primordial seed
fluctuations, the physics of inflation remains one of the biggest open problems in cosmology and
fundamental physics.
An intriguing feature of inflation is that our view of this epoch is frozen in time. We can only make inferences
about the inflationary era from spatial correlations of the primordial fluctuations for the post-inflationary
universe. These primordial correlations live on the future boundary of the inflationary spacetime or,
equivalently, the past boundary of the hot Big Bang universe. Learning how to extract the dynamics of
inflation from these static boundary correlations is an essential goal of modern cosmology.
The standard approach to compute inflationary correlators is to follow their time evolution from early times to
the end of inflation. However, this requires assumptions about the interactions during inflation, and often
leads to overly complicated computations. Alternatively, we can try to understand which principles constrain
the inflationary physics and, thus, which rules the inflationary correlation functions ought to satisfy. This is
precisely the point of view which has been extremely successful in the study of both conformal field theories
and scattering amplitudes in asymptotically flat spacetimes, and in recent years it has also started to be
applied to cosmology: rather than relying on the explicit time evolution, correlators can be directly computed
at the end of inflation via consistency with symmetries, unitarity (i.e. the statement that probabilities have to
sum up to one), and with the flat-space limit. The consequences of unitary time evolution are now understood
in the perturbative regime, i.e. when the interactions are small, and even some initial progress has been
made on extensions to the nonperturbative regime. The consistency conditions and principles uncovered by
studyingkprimordial fluctuations, along with the necessity to incorporate gravitational eflects at quantum level
during the inflation, may deepen our understanding of what constitutes a truly consistent inflationary theory.
When combined with the conjectured equivalence, known askholography, betweenknon-gravitating quantum
systems and theories of quantum gravity, insight toward the underlying degrees of freedom of an inflationary
spacetime may be revealed.
While these developments are indeed exciting, they have clearly just scratched the surface of an important
topic, and we have only started to develop the tools to answer deep physical questions. More interaction
between researchers with diflerent expertise is needed to make further progress. This program precisely
aims to boost such interactions, involving experts in theoretical cosmology, quantum field theory in curved
spacetimes, scattering amplitudes, eflective field theories, non-perturbative bootstrap, holography as well as
mathematics.