Covariant Formulation of the Invariant Measure for the Mixmaster Dynamics

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. We construct the appropriate invariant measure for the system (which relies on the existence of an ``energy-like'' constant of motion) without fixing the time gauge, i.e. the corresponding lapse function. The key point in our analysis consists of introducing generic Misner-Chitr\'e-like variables containing an arbitrary function, whose specification allows one to set up the same dynamical scheme in any time gauge.Comment: 11 pages, 1 figur

Cosmological implications of an evolutionary quantum gravity

The cosmological implications of an evolutionary quantum gravity are analyzed in the context of a generic inhomogeneous model. The Schr\"{o}dinger problem is formulated and solved in the presence of a scalar field, an ultrarelativistic matter and a perfect gas regarded as the dust-clock. Considering the actual phenomenology, it is shown how the evolutionary approach overlaps the Wheeler-DeWitt one.Comment: 4 pages; to appear in the proceedings of the II Stueckelberg Workshop, Int.J.Mod.Phys.A, references adde

Synchronous Quantum Gravity

The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schr\"odinger Quantum Gravity with respect to the asymptotically early dynamics of a generic Universe. A dualism between time and the reference frame fixing is then inferred.Comment: 8 pages, Proceedings of the II Stueckelberg worksho

Towards Loop Quantum Gravity without the time gauge

The Hamiltonian formulation of the Holst action is reviewed and it is provided a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the Loop Quantum Gravity quantization procedure can be applied when the time-gauge condition does not stand.Comment: 5 pages, accepted for publication in Phys. Rev. Let

Dark Matter Prediction from Canonical Quantum Gravity with Frame Fixing

We show how, in canonical quantum cosmology, the frame fixing induces a new energy density contribution having features compatible with the (actual) cold dark matter component of the Universe. First we quantize the closed Friedmann-Robertson-Walker (FRW) model in a sinchronous reference and determine the spectrum of the super-Hamiltonian in the presence of ultra-relativistic matter and a perfect gas contribution. Then we include in this model small inhomogeneous (spherical) perturbations in the spirit of the Lemaitre-Tolman cosmology. The main issue of our analysis consists in outlining that, in the classical limit, the non-zero eigenvalue of the super-Hamiltonian can make account for the present value of the dark matter critical parameter. Furthermore we obtain a direct correlation between the inhomogeneities in our dark matter candidate and those one appearing in the ultra-relativistic matter.Comment: 5 pages, to appear on Modern Physics Letters

Lifshitz fermionic theories with z=2 anisotropic scaling

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.Comment: Typos corrected, comment adde

Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework

The implications of a Generalized Uncertainty Principle on the Taub cosmological model are investigated. The model is studied in the ADM reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a canonical way and the only physical degree of freedom of the system (related to the Universe anisotropy) is quantized by means of a modified Heisenberg algebra. The analysis is performed at both classical and quantum level. In particular, at quantum level, the motion of wave packets is investigated. The two main results obtained are as follows. i) The classical singularity is probabilistically suppressed. The Universe exhibits a stationary behavior and the probability amplitude is peaked in a determinate region. ii) The GUP wave packets provide the right behavior in the establishment of a quasi-isotropic configuration for the Universe.Comment: 10 pages, 4 figures; v2: section added, to appear on PR

Dualism between Physical Frames and Time in Quantum Gravity

In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as first step, we develop the canonical quantum dynamics, starting from the Einstein equations in presence of a dust fluid and arrive to a Schroedinger evolution. Then, by fixing the lapse function in the path integral of gravity, we get a Schroedinger quantum dynamics, of which eigenvalues problem provides the appearance of a dust fluid in the classical limit. The main issue of our analysis is to claim that a theory, in which the time displacement invariance, on a quantum level, is broken, is indistinguishable from a theory for which this symmetry holds, but a real reference fluid is included.Comment: 9 pages, submitted to Mod. Phys. Lett. A, major replacements in section 3 and