Multidimensional Physics - Quant. Gravity - Early Cosmology

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The attempt to represent Gravitation as a real gauge theory is motivated by the possibility to extend the algorithms of Yang-Mills fields quantization to the space-time geometry. In this line of thinking we investigate the so-called “frozen formalism” problem affecting the canonical quantum gravity. In fact, the super-Hamiltonian constraint prevents the theory from having a real time evolution and this feature strikingly distinguishes gravity from gauge theories. Addressing different points of view, we have shown how a dualism exists in quantum gravity between breaking explicitly the invariance under time displacements and including in the dynamics a reference fluid. The phenomenological issues of this evolutionary approach to the quantum dynamics of the 3-metric tensor could provide us with a new candidate for the cold dark matter; in fact the classical limit taken on the super-Hamiltonian eigenvalue yields a dust energy density involved in the cosmological dynamics.

Main publications:

- G. Montani, Canonical Quantization of Gravity without Frozen Formalism, Nucl. Phys. B, 634, 370 (2002) [gr-qc/0205032] [pdf].

- S. Mercuri and G. Montani, Revised Canonical Quantum Gravity via the Frame Fixing, Int. J. Mod. Phys. D, 13, 165 (2004) [gr-qc/0310077] [pdf].

- S. Mercuri and G. Montani, Dualism between Physical Frames and Time in Quantum Gravity, Mod. Phys. Lett. A, 19, 1519 (2004) [gr-qc/0312077] [pdf].

- M.V. Battisti and G. Montani, Evolutionary Quantum Dynamics of a Generic Universe, Phys. Lett. B, 637, 203 (2006) [gr-qc/0604049] [pdf].

- R. Benini and G. Montani, Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics, Class. Quant. Grav., 24, 387 (2007) [gr-qc/0612095] [pdf].