Cosmic Inflation, Quantum Information and the Pioneering Role of John S
  Bell in Cosmology
  According to the theory of cosmic inflation, the large scale structures
observed in our Universe (galaxies, clusters of galaxies, Cosmic Background
Microwave - CMB - anisotropy ...) are of quantum mechanical origin. They are
nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic
expansion and amplified by gravitational instability. At the end of inflation,
these perturbations are placed in a two-mode squeezed state with the strongest
squeezing ever produced in Nature (much larger than anything that can be made
in the laboratory on Earth). This article studies whether astrophysical
observations could unambiguously reveal this quantum origin by borrowing ideas
from quantum information theory. It is argued that some of the tools needed to
carry out this task have been discussed long ago by J. Bell in a, so far,
largely unrecognized contribution. A detailed study of his paper and of the
criticisms that have been put forward against his work is presented. Although
J. Bell could not have realized it when he wrote his letter since the quantum
state of cosmological perturbations was not yet fully characterized at that
time, it is also shown that Cosmology and cosmic inflation represent the most
interesting frameworks to apply the concepts he investigated. This confirms
that cosmic inflation is not only a successful paradigm to understand the early
Universe. It is also the only situation in Physics where one crucially needs
General Relativity and Quantum Mechanics to derive the predictions of a theory
and, where, at the same time, we have high-accuracy data to test these
predictions, making inflation a playground of utmost importance to discuss
foundational issues in Quantum Mechanics
