Lorentz Violation of Quantum Gravity

A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns $SO(3,1)\to O(3)$ and $SO(3,1)\to O(2)$, describing 3+1 and 2+1 quantum gravity, respectively, is proposed. A complex time dependent Schr\"odinger equation (generalized Wheeler-DeWitt equation) for the wave function of the universe exists in the spontaneously broken symmetry phase at Planck energy and in the early universe, uniting quantum mechanics and general relativity. An explanation of the second law of thermodynamics and the spontaneous creation of matter in the early universe can be obtained in the symmetry broken phase of gravity.Comment: 10 pages, minor change and reference added. Typos corrected. To be published in Class. Quant. Grav

Einstein-aether as a quantum effective field theory

The possibility that Lorentz symmetry is violated in gravitational processes is relatively unconstrained by experiment, in stark contrast with the level of accuracy to which Lorentz symmetry has been confirmed in the matter sector. One model of Lorentz violation in the gravitational sector is Einstein-aether theory, in which Lorentz symmetry is broken by giving a vacuum expectation value to a dynamical vector field. In this paper we analyse the effective theory for quantised gravitational and aether perturbations. We show that this theory possesses a controlled effective expansion within dimensional regularisation, that is, for any process there are a finite number of Feynman diagrams which will contribute to a given order of accuracy. We find that there is no log-running of the two-derivative phenomenological parameters, justifying the use of experimental constraints for these parameters obtained over many orders of magnitude in energy scale. Given the stringent experimental bounds on two-derivative Lorentz-violating operators, we estimate the size of matter Lorentz-violation which arises due to loop effects. This amounts to an estimation of the natural size of coefficients for Lorentz-violating dimension-six matter operators, which in turn can be used to obtain a new bound on the two-derivative parameters of this theory.Comment: 21 page

Quantum Spacetime Phenomenology

I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. And my main focus is on phenomenological programs that managed to affect the directions taken by studies of quantum-spacetime theories.Comment: 125 pages, LaTex. This V2 is updated and more detailed than the V1, particularly for quantum-spacetime phenomenology. The main text of this V2 is about 25% more than the main text of the V1. Reference list roughly double