New counterterms induced by trans-Planckian physics in semiclassical gravity

Abstract

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.

References in corpus (21)

• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Gravity with a dynamical preferred frame
• The Trans-Planckian Problem of Inflationary Cosmology
• Einstein-Aether Waves
• Lorentz-Violating Vector Fields Slow the Universe Down
• The Robustness of Inflation to Changes in Super-Planck-Scale Physics
• Lorentz invariance and quantum gravity: an additional fine-tuning problem?
• Inflation with a Planck-scale frequency cutoff
• On the Dependence of the Spectra of Fluctuations in Inflationary Cosmology on Trans-Planckian Physics
• Trans-Planckian dispersion and scale-invariance of inflationary perturbations
• Post-Newtonian parameters and constraints on Einstein-aether theory
• Can We See Lorentz-Violating Vector Fields in the CMB?
• Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars
• Back-Reaction and the Trans-Planckian Problem of Inflation Revisited
• Detecting a Lorentz-Violating Field in Cosmology
• Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem
• Quantum Corrections to Lorentz Invariance Violating Theories: Fine-Tuning Problem
• A momentum-space representation of Green's functions with modified dispersion on ultra-static space-time
• Backreaction in trans-Planckian cosmology: renormalization, trace anomaly and selfconsistent solutions
• Renormalized Stress Tensor for trans-Planckian Cosmology
• Adiabatic renormalization in theories with modified dispersion relations

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• On the renormalization procedure for quantum fields with modified dispersion relation in curved spacetimes
• Induced energy-momentum tensor of Dirac field in 2D de Sitter QED