Over the last decades, conformal field theory (CFT) technics have played an important role in black hole physics, due to the discovery of unexpected conformal symmetries in the near horizon of black hole. Using these technics, crucial features of black hole physics, among which their spectroscopy, quasi-normal modes, as well as their state counting have been reproduced using CFT technics.
So far, the possible existence of similar hidden conformal symmetry in cosmological spacetimes have been much less investigated.
In this talk, I will show that the simplest cosmological model, consisting in the homogeneous and isotropic Einstein-Scalar system, enjoys a surprising hidden conformal symmetry. I will present in detail this new structure, the associated Noether's charge as well as the CVH algebra which encodes this conformal symmetry at the hamiltonian level.
Then, I will explain how this cosmological system can be mapped to the well known conformal mechanics developed by de Alfaro, Fubini and Furlan, and which provides the simplest example of a classically conformal field theory in 1d.
This conformal structure extends beyond this simple homogeneous and isotropic setting. I will briefly discuss the inclusion of a cosmological constant, anisotropies, self-interacting potential for the scalar field, as well as work in progress on the fully inhomogeneous Einstein-Scalar system.
Finally, I will discuss the consequences of this new conformal structure at the quantum level. A major outcome is the possibility to apply the conformal bootstrap program to quantize the theory. Just as quantum conformal mechanics, I will show that despite the lack of a conformally invariant group state, it is possible to find an operator which reproduces the standard form of the CFT two points function in quantum cosmology. I will discuss the cosmological interpretation of this operator and the vacuum state which are used to construct this correlator.
In the end, this provides a first step to bootstrap quantum cosmology using this new conformal symmetry.
Based on: arXiv:1909.13390.