Adiabatic renormalization in theories with modified dispersion relations

Abstract

We generalize the adiabatic renormalization to theories with dispersion relations modified at energies higher than a new scale $M_C$. We obtain explicit expressions for the mean value of the stress tensor in the adiabatic vacuum, up to the second adiabatic order. We show that for any dispersion relation the divergences can be absorbed into the bare gravitational constants of the theory. We also point out that, depending on the renormalization prescription, the renormalized stress tensor may contain finite trans-Planckian corrections even in the limit $M_C\to \infty$.

Typos corrected; to appear in the Proceedings of IRGAC 06, Journal of Physics A

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• Aspects of Quantum Gravity in Cosmology
• Induced energy-momentum tensor of Dirac field in 2D de Sitter QED
• Energy-momentum tensor and effective Lagrangian of scalar QED with a nonminimal coupling in 2D de Sitter spacetime