On the Frame Fixing in Quantum Gravity

We provide a discussion about the necessity to fix the reference frame before quantizing the gravitational field. Our presentation is based on stressing how the 3+1-slicing of the space time becomes an ambiguous procedure as referred to a quantum 4-metric.Comment: 3 pages, no figures, proceeding of the X Marcel Grossmann meeting, Rio de Janeiro, Brazil, July 20-26, 200

A New Approach in Quantum Gravity and its Cosmological Implications

This work concerns a new reformulation of quantum geometrodynamics, which allows to overcome a fundamental ambiguity contained in the canonical approach to quantum gravity: the possibility of performing a (3+1)-slicing of space-time, when the metric tensor is in a quantum regime. Our formulation provides also a procedure to solve the problems connected to the so called "frozen formalism". In particular we fix the reference frame (i.e. the lapse function and the shift vector) by introducing the so called "kinematical action"; as a consequence, the new hamiltonian constraints become parabolic, so arriving to evolutive (Schroedinger-like) equations for the quantum dynamics. The kinematical action can be interpreted as the action of a pressureless, but, in general, non geodesic perfect fluid, so in the semi classical limit our theory leads to the dynamics of the gravitational field coupled to a dust which represents the material reference frame we have introduced fixing the slicing. We also investigate the cosmological implications of the presence of the dust, which, in the WKB limit of a cosmological problem, makes account for a "dark matter" component and could play, at present time, a dynamical role.Comment: A synthesis of previous works, based on a talk given at the VIII Italian-Korean meeting (Pescara, Italy), to appear on "Il Nuovo Cimento

Modifications in the Spectrum of Primordial Gravitational Waves Induced by Instantonic Fluctuations

Vacuum to vacuum instantonic transitions modify the power spectrum of primordial gravitational waves. We evaluate the new form of the power spectrum for ordinary gravity as well as the parity violation induced in the spectrum by a modification of General Relativity known as Holst term and we outline the possible experimental consequences.Comment: V1: 8 pages. V2: 8 pages, some points clarified, typos corrected, some references added, final result unchanged. V3: 8 pages, title changed, presentation improved, discussion of phenomenological consequences added, comments very welcome. V4: Discussion further improved, comments very very welcom

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

From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional

The Ashtekar-Barbero constraints for General Relativity with fermions are derived from the Einstein-Cartan canonical theory rescaling the state functional of the gravity-spinor coupled system by the exponential of the Nieh-Yan functional. A one parameter quantization ambiguity naturally appears and can be associated with the Immirzi parameter.Comment: Minor changes, two references added, accepted for publication in Phys. Rev.