The aim of this thesis is the study of the quantum to classical transition
with a particular interest to quantum to classical gravity.
Of fundamental importance are the imprints left from quantum phenomenon
in the observed signal, such as CMB anisotropies and gravitational waves.

Quantum gravity is a hard task to tackle head-on.
Electromagnetism however is a case in which such a transition is well grounded this is the reason why,
as a starting point, we will consider the well known case of the electromagnetic field.
Indeed, when a large number of photons are involved the field can be
described as a statistical system thanks to the formalism
of coherent states built by R. Glauber and G. Sudarshan in the early
60'.  Glauber-Sudarshan coherent states, defined as the proper states of
the annihilation operator, are known to constitute an over-complete basis
of states of the Fock space and to exhibit many specific properties amongst
them the saturation of the Heisenberg inequality (quasi-classical states).
They allow to define the notion of coherence at the quantum level, and to
built a representation of operators, from which classical quantities can
be recovered as a limit.

The transition from quantum to classical for electromagnetism, within this
framework of coherent states, will act as a guideline for the case of gravity.
It is noteworthy that (very) recent works make use of similar tools in
analyzing gravitational waves [1] or CMB fluctuations [2].
The relation with effective or emergent theories can also be envisaged.

[1] R. Britto, R. Gonzo and G. R. Jehu "Graviton particle statistics and coherent states from
classical scattering amplitudes", JHEP03, 214 (2022).

[2] M. Giovannini, "Glauber theory and the quantum coherence of curvature inhomogeneities",
Class.Quant.Grav. 34, 035019, (2017), e-Print: 1608.05843 [hep-th]