New counterterms induced by trans-Planckian physics in semiclassical gravity

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}

. We argue that, in a general spacetime, the renormalization of the theory would involve new counterterms constructed with

g_{\mu\nu}

and

u_{\mu}

, generating a fine-tuning problem for the Einstein-Aether theory.

04.62.+v
11.10.Gh
98.80.Cq
field theory: scalar
field theory: vector
tensor: energy-momentum
renormalization: finite
expansion: adiabatic
violation: Lorentz
space-time: Robertson-Walker

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