TL;DR
This paper embeds deformed special relativity within deformed general relativity using canonical methods, revealing phase-space dependent symmetry deformations that could aid in testing loop quantum gravity.
Contribution
It introduces a novel approach to derive deformations with clear physical roles from canonical constraints, avoiding issues in momentum space and macroscopic objects.
Findings
Deformations appear as non-linear Poincare algebras with momentum-dependent features.
No non-locality issues arise from the deformations.
Potential for experimental tests of loop quantum gravity.
Abstract
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be rewritten as non-linear Poincare algebras with momentum-dependent deformations of commutators between boosts and time translations. In contrast to deformed special relativity, the deformations are derived for generators with an unambiguous physical role, following from the relationship between canonical constraints of gravity with stress-energy components. The original deformation does not appear in momentum space and does not give rise to non-locality issues or problems with macroscopic objects. Contact with deformed special relativity may help to test loop quantum gravity or restrict its quantization ambiguities.
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