The authors describe classical models of gravitation interacting with scalar fields whose solutions involve degenerate metrics. Some of these solutions exhibit transitions from a Euclidean domain to a Lorentzian spacetime corresponding to a spatially flat Robertson-Walker cosmology.

We propose a new law for the deceleration parameter that varies linearly with time and covers Berman's law where it is constant. Our law not only allows one to generalize many exact solutions that were obtained assuming constant deceleration parameter, but also gives a better fit with data (from SNIa, BAO and CMB), particularly concerning the late time behavior of the universe. According to our law only the spatially closed and flat universes are allowed; in both cases the cosmological fluid we obtain exhibits quintom like behavior and the universe ends with a big-rip. This is a result consistent with recent cosmological observations.

We investigate the non-minimal couplings between the electromagnetic fields and gravity through the natural logarithm of the curvature scalar. After we give the Lagrangian formulation of the non-minimally coupled theory, we derive field equations by a first order variational principle using the method of Lagrange multipliers. We look at static, spherically symmetric solutions that are asymptotically flat. We discuss the nature of horizons for some candidate black hole solutions according to various values of the parameters R 0 and a 1 .

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature. -2 - IntroductionNon-Riemannian geometries feature in a number of theoretical descriptions of the interactions between fields and gravitation. Since the early pioneering work by Weyl, Cartan, Schroedinger and others such geometries have often provided a succinct and elegant guide towards the search for unification of the forces of nature [1]. In recent times interactions with supergravity have been encoded into torsion fields induced by spinors and dilatonic interactions from low energy effective string theories have been encoded into connections that are not metric-compatible [2], [3], [4], [5]. However theories in which the non-Riemannian geometrical fields are dynamical in the absence of matter are more elusive to interpret. It has been suggested that they may play an important role in certain astrophysical contexts [6]. Part of the difficulty in interpreting such fields is that there is little experimental guidance available for the construction of a viable theory that can compete effectively with general relativity in domains that are currently accessible to observation. In such circumstances one must be guided by the classical solutions admitted by theoretical models that admit dynamical non-Riemannian structures [7], [8], [9], [10], [11]. A number of recent papers have pursued this approach and have found static spherically symmetric solutions to particular models [12], [13]. In [6] it was pointed out that in a particularly simple model all EinsteinMaxwell solutions to general relativity could be used to generate dynamic non-Riemannian geometries and a tentative interpretation was offered for the matter couplings in such a model. Particular solutions have also been found to more complex models, provided the coupling constants in the action are correlated [12], [13], [14], [15]. It is the purpose of this note to point out that, if such correlations are maintained then solutions may be generated from all Einstein-Maxwell solutions of general relativity. Furthermore the correlations may be discarded and solutions generated from all Einstein-Proca solutions of general relativity with or without the inclusion of a cosmological term in the action.

The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan space-time and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass eigenstates are found. These effects are of the order of Planck scales.

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The authors exhibit a family of Hilbert subspaces describing solutions to the Wheeler-DeWitt equation. Each subspace describes a distinct quantum theory in which the parameters of the potential are required to satisfy a particular 'quantization' condition. Tentative evidence suggests that within each Hilbert subspace there exist states that may be identified with nondispersive wave packets peaking in the vicinity of submanifolds in superspace corresponding to classical cosmological eras. These submanifolds admit parameterizations corresponding to metric solutions of Einstein's equations that admit a transition between a Euclidean and a Lorentzian signature.

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