International Journal of Modern Physics D

The general problems of three-dimensional quantum gravity are recapitulated here, with emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics. This work should be viewed as an extension of a preceding one on the four-dimensional case,¹² where some general ideas were also discussed in detail. We finally put forward some suggestions on the lines where one could expect further progress in the field.

A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac observables, i.e. phase-space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through “deparametrization” and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory in spite of the fact that the evolution is implemented by a one-parameter family of unitary transformations. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to the quantum theory following an independent avenue. The two quantum theories — based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables — are compared and shown to be equivalent.

The path integral for higher-derivative quantum gravity with torsion is considered. Applying the methods of two-dimensional quantum gravity, this path integral is analyzed in the limit of conformally self-dual metrics. A scaling law for fixed-volume geometry is obtained.

The classical and the quantum scattering of two maximally-charged dilaton black holes which have low velocities are studied. We find a critical value for the dilaton coupling, a²=1/3. For a²>1/3, two black holes are always scattered away and never coalesce together, regardless of the value of the impact parameter.

We discuss the classical change of signature in Rindler space modified according to a model with maximal acceleration. This fact acquires great interest in quantum cosmology, when one considers the wave function of the universe tunneling from the Euclidean regime to the Lorentzian one.

String effective theories contain a dilaton scalar field which couples to gravity, matter and radiation. In general, particle masses will have different dilaton couplings. We can always choose a conformal frame in which baryons have constant masses while (nonbaryonic) dark matter have variable masses, in the context of a scalar-tensor gravity theory. We are interested in the phenomenology of this scenario. Dark matter with variable masses could have a measurable effect on the dynamical motion of the halo of spiral galaxies, which may affect cold dark matter models of galaxy formation. As a consequence of variable masses, the energy-momentum tensor is not conserved; there is a dissipative effect, due to the dilaton coupling, associated with a “dark entropy” production. In particular, if axions had variable masses they could be diluted away, thus opening the “axion window.” Assuming that dark matter with variable masses dominates the cosmological evolution during the matter era, it will affect the primordial nucleosynthesis predictions on the abundances of light elements. Furthermore, the dilaton also couples to radiation in the form of a variable gauge coupling. Experimental bounds will constrain the parameters of this model.

The anisotropy properties of the Cosmic Microwave Background Radiation (CMB) are considered within the framework of the photon beam mixing effect developed earlier. The existence of an observable characteristic of the CMB is shown, namely the geometrical shape of anisotropy spots and their degree of complexity, which can contain unique information on cosmological parameters and the life history of the Universe. If future experiments (COBE and others) indicate such features of anisotropy maps, then one can have serious evidence for the negative curvature of the Universe.

We extend to higher dimensions an earlier work of Letelier where a Bianchi type I cosmological model with massive strings as source term is studied. Exact solutions are obtained assuming either an equation of state between the energy density and tension density of the string or an explicit form of one of the metric coefficients. The dynamical behavior of the models is studied and a comparison is made with the analogous four-dimensional case where it is interestingly observed that the string dominated phase lasts a longer period in multidimensional models compared to its four-dimensional analogs. The Kantowski-Sachs type of metric is also briefly discussed.

We study the formation of structure for a universe that undergoes a recent loitering phase. We compare the nonlinear mass distribution to that in a standard, matter dominated cosmology. The statistical aspects of the clustered matter are found to be robust to changes in the expansion law, an exception being that the peculiar velocities are lower by a factor of ~3 in the loitering model. Further, in the loitering scenario, nonlinear growth of perturbation occurs more recently (z~3–5) than in the matter dominated case. Differences in the high redshift appearances of the two models will result but observable consequences depend critically on the chosen form, onset and duration of the loitering phase.

We consider an addition of the term which is a square of the scalar curvature to the Einstein-Hilbert action. Under this generalized action, we attempt to explain (i) the flat rotation curves observed in spiral galaxies, which is usually attributed to the existence of dark matter, and (ii) the contradicting observations of the uniform cosmic microwave background and the nonuniform galaxy distributions against redshift. For the former, we attain the flatness of velocities, although the magnitudes remain about half that of the observations. For the latter, we obtain a solution with the oscillating Hubble parameter under uniform mass distributions. This solution leads to several peaks of galaxy number counts as a function of redshift with the first peak corresponding to the Great Wall.