Observational constraints on the quantum Einstein-Aether model

We build a classical cosmological model by applying the ADM formalism to a modified theory of gravitation, based on General Relativity. The Einstein-Aether theory couples a timelike vector field to the metric, selecting a preferred local frame of reference and thus breaking the Lorentz symmetry. The intensity of this coupling is determined by dimensionless constants, and in this work, the values of these constants were chosen in accordance with the existing theoretical and observational constraints. The use of the ADM formalism generates the loss of a time-type variable known as the “time problem” which, in this work, is approached phenomenologically by the introduction of the material content of the Universe as a perfect baryonic fluid. This is the so-called Schutz formalism, in which this fluid is described by six potential fields, and a new time-like variable is defined from the fluid entropy. We consider a general model, for any perfect baryonic fluid, in a homogeneous and isotropic FLRW Universe. This cosmological model has two degrees of freedom: the scale factor a and the time \(\tau \). The Wheeler-DeWitt quantization scheme is then applied, and the wave function of the Universe is obtained. In this work we consider the solutions of the Wheeler-DeWitt equation that satisfy the boundary condition in which the derivative of the wave function at \(a=0\) is zero. We apply to this quantum cosmological model the many-worlds interpretation and the de Broglie-Bohm interpretation of quantum mechanics, verifying the possibility of avoiding a singularity at the beginning of the Universe.