FLRW cosmology as a conformal field theory in one dimension

Over the last decades, a vast set of results have shown that the near horizon region of black holes enjoys an unexpected conformal symmetry, allowing to provide an effective conformal description of the thermodynamical properties of these black holes. Additional surprising conformal structures have been found for test particles propagating on the near horizon region of various black hole spacetimes, allowing to reproduce several crucial features of these compact objects such as their spectroscopy, quasi-normal modes as well as their state counting using conformal field theory (CFT) technics. Just as black hole, cosmological spacetimes admit a thermodynamical interpretation. They are equipped with an entropy and their horizon radiate at a temperature given by their surface gravity. One could naturally wonder whether these thermodynamical properties can also be describe by CFT technics, just as for their black hole cousins. Recently, efforts have been devoted to investigate, from various perspectives, whether cosmological backgrounds exhibit also some hidden conformal symmetry. In this talk, I will show that, indeed, the simplest cosmological model consisting in the homogeneous and isotropic Einstein-Scalar system enjoys a new unexpected conformal symmetry. I will present in detail this symmetry, the new Noether's charges to this hidden conformal invariance and the associated CVH algebra which encodes this structure at the hamiltonian level. Then, I will also show that this cosmological system can be mapped to the so called conformal mechanics of de Alfaro, Fubini and Furlan, which provides the simplest example of a conformal field theory in 1d. Finally, I will discuss the consequences of this new conformal structure at the quantum level and how the standard form of the CFT two points function emerge in quantum cosmology.