The semiclassical formulation of gravity is discussed in the framework of algebraic quantum field theory in curved spacetimes. The main topic of the talk is the Semiclassical Einstein Equations, which describe the backreaction of a quantum scalar field on spacetime geometry. In the first part of the talk, it is shown that an initial-value problem for local solutions of the Semiclassical Einstein Equations can be formulated in cosmological spacetimes, after fixing four initial data on the scale factor of the Universe. In the second part of the talk, it is studied the problem of stability of linearized solutions, using a toy model which mimics the semiclassical equations in cosmological spacetimes. In this case, it is proved that, if the quantum field driving the backreaction is massive, then there are choices of renormalization constants for which linear perturbations with compact spatial support decay for large times, thus indicating stability of the underlying theory [arXiv:2007.14665, 2201.10288].
A video recording of the event is available at: https://wigner.videotorium.hu/hu/recordings/49617