Holographie, horizons cosmologiques et information quantique en gravité quantique

In quantum gravity, when the holographic principle is applicable, it states that a gravitational theory defined in a given spacetime can be fully described by a non-gravitational theory located on a suitable boundary of that spacetime. To date, the AdS/CFT correspondence provides the most complete illustration of this principle. In this framework, the existence of a non-gravitating spatial boundary allows placing the observer at infinity, so that it does not backreact on the geometry and physical observables are well-defined in terms of field correlators on the boundary. A natural question then arises: Can an analogous holographic principle apply to more realistic universes, and in particular to de Sitter-type spacetimes? In this case, major conceptual difficulties appear. Since the universe is of finite size, any observer is necessarily located within space, with its own mass, entropy, and clock, and inevitably backreacts on the geometry. Thus, a quantum theory of gravity in such a closed universe cannot ignore the observer, who must be included as part of the dynamical system. Moreover, a de Sitter spacetime does not possess a spatial boundary in the usual sense, making any direct application of the holographic principle problematic and raising the fundamental question of the hologram's localization. However, this issue, together with the previous difficulty, suggests an approach. Every inertial observer in de Sitter spacetime is associated with a cosmological horizon, which delimits the region of spacetime that is causally accessible to him. Longstanding and robust arguments indicate that this horizon plays a fundamental thermodynamic role. In particular, Gibbons and Hawking showed that for such an observer, the de Sitter vacuum appears as a thermal state characterized by a temperature set by the cosmological horizon, and that the gravitational entropy associated with the causally accessible region is proportional to the area of this horizon rather than to the volume of the region. This makes it conceivable to consider the cosmological horizon as an effective boundary, specific to each observer.