AG Mathematische Physik: Paolo Meda (Trento): The Semiclassical Einstein Equations and the Stability of Linearized Solutions

Paolo Meda (Trento)

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 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].