New counterterms induced by trans-Planckian physics in semiclassical gravity

Understand

We consider free and self-interacting quantum scalar fields satisfying modified dispersion relations in the framework of Einstein-Aether theory.

• Using adiabatic regularization, we study the renormalization of the equation for the mean value of the field in the self-interacting case, and the renormalization of the semiclassical Einstein-Aether equations for free fields.
• In both cases we consider Bianchi type I background spacetimes.
• Contrary to what happens for {\it free} fields in {\it flat} Robertson-Walker spacetimes, the self-interaction and/or the anisotropy produce non-purely geometric terms in the adiabatic expansion, i.e terms that involve both the metric $g_{\mu\nu}$ and the aether field $u_{\mu}$.