The Semiclassical Einstein Equations and the Stability of Linearized Solutions

Abstract: 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 field on the spacetime geometry. In the first part of the talk, it is shown that an initial-value problem for the semiclassical Einstein equations can be formulated in cosmological spacetimes for a small interval of time, 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 there are choices of renormalization parameters for which linear perturbations decay in time for large times, thus indicating stability of the underlying theory. [arXiv:2007.14665, 2201.10288].