Gravitation might make a preferred frame appear, and with it a clear space/time separation?the latter being, a priori, needed by quantum mechanics (QM) in curved space-time. Several models of gravitation with an ether are discussed: they assume metrical effects in an heterogeneous ether and/or a Lorentz-symmetry breaking. One scalar model, starting from a semi-heuristic view of gravity as a pressure force, is detailed. It has been developed to a complete theory including continuum dynamics, cosmology, and links with electromagnetism and QM. To test the theory, an asymptotic scheme of post-Newtonian approximation has been built. That version of the theory which is discussed here predicts an internal-structure effect, even at the point-particle limit. The same might happen also in general relativity (GR) in some gauges, if one would use a similar scheme. Adjusting the equations of planetary motion on an ephemeris leaves a residual difference with it; one should adjust the equations using primary observations. The same effects on light rays are predicted as with GR, and a similar energy loss applies to binary pulsars.
We consider three versions of the Dirac equation in a curved spacetime: the standard (Dirac-Fock-Weyl or DFW) equation, and two alternative versions. Both of these alternative versions are based on the recently proposed tensor representation of the Dirac field (TRD), that considers the Dirac wave function as a spacetime vector and the set of the Dirac matrices as a third-order tensor [1-3]. These three equations differ also in the covariant derivative D?. A common tool for the study is the Bargmann-Pauli hermitizing matrix A. Having the current conservation for any solution of the Dirac equation gives an equation to be satisfied by the fields (g m, A), with g m the Dirac matrices. This condition is always verified for DFW with its restricted choice for the field g m. It similarly restricts the choice of the field g m for TRD. However, this restriction can be achieved. A positive definite scalar product is defined and a hermiticity condition for the Dirac Hamiltonian is derived for a general coordinate system with minor restrictions, in a general curved spacetime. For DFW, the hermiticity of the Dirac Hamiltonian is not preserved under all admissible changes of the fields (g m, A).
Some motivation for an ether theory of gravitation is presented. The equations of one such theory, based on just one scalar field, are given. It is a preferred-frame theory with a flat background metric and a curved physical metric. Motion is governed by an extension of the special-relativistic form of Newton’s second law. The current status of the observational test is favourable. In particular, the new theory reduces to Newton’s when it has to, and it does explain the effects of gravitation on light rays. In the most general form of the metric, cosmic space expansion occurs with a cosmological time-dilation. Expansion is necessarily accelerated, according to that theory. An analytical cosmological solution is got for a general form of the matter tensor. Two kinds of scenarios are possible: either expansion from an infinite density at past infinity, or contraction-expansion cycles beginning and ending with infinite dilution, and with a bounce at a finite maximum density. In the most likely scenario, there is an infinite number of non-identical such cycles. The time scale for the current cycle is very large.