New counterterms induced by trans-Planckian physics in semiclassical gravity

D. LÓPEZ NACIR; F. D. MAZZITELLI

João Pessoa, Brasil.

Otro; Seventh Alexander Friedmann International Seminar on Gravitation and Cosmology.; 2008

Universidad Federal de Paraiba -UFPb (Brazil)

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 free fields in 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.