Adiabatic renormalization in theories with modified dispersion relations

TL;DR

This paper extends adiabatic renormalization techniques to theories with modified high-energy dispersion relations, providing explicit formulas for stress tensor renormalization and discussing implications for trans-Planckian effects.

Contribution

It generalizes adiabatic renormalization to theories with modified dispersion relations and derives explicit expressions for stress tensor renormalization up to second order.

Findings

Divergences are absorbable into gravitational constants.

Renormalized stress tensor may include finite trans-Planckian corrections.

Explicit formulas for stress tensor in modified dispersion theories.

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 $M_C\to\infty$.