The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System

Understand

We develop a comprehensive framework in which the existence of solutions to the semiclassical Einstein equation (SCE) in cosmological spacetimes is shown.

• Different from previous work on this subject, we do not restrict to the conformally coupled scalar field and we admit the full renormalization freedom.
• Based on a regularization procedure, which utilizes homogeneous distributions and is equivalent to Hadamard point-splitting, we obtain a reformulation of the evolution of the quantum state as an infinite-dimensional dynamical system with mathematical features that are distinct from the standard theory of infinite-dimensional dynamical systems (e.g., unbounded evolution operators).
• Nevertheless, applying methods closely related to Ovsyannikov's method, we show existence of maximal/global solutions to the SCE for vacuum-like states, and of local solutions for thermal-like states.