Lorentz Violation of Quantum Gravity

Abstract

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 Schrödinger 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.

10 pages, minor change and reference added. Typos corrected. To be published in Class. Quant. Grav.

References in corpus (4)

• Quantum Gravity at a Lifshitz Point
• Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology
• Quantum Gravity, the Origin of Time and Time's Arrow
• Spontaneous Violation of Lorentz Invariance and Ultra-High Energy Cosmic Rays

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• Renormalizing gravity: a new insight into an old problem
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• Probing the interference between non-linear, axionic and space-time-anisotropy effects in the QED vacuum
• Gravitational Entropy and the Second Law of Thermodynamics
• Bounds on Vacuum-Orthogonal Lorentz and CPT Violation from Radiative Corrections
• Lorentz-symmetry violation in the electroweak sector: scattering processes in future $e^{+}{e}^{-}$ colliders