Cosmic Strings and Negative $$\Lambda $$: Probing the Infant Universe in Einstein-Æther Theory

In this work, we analyze a quantized cosmological model within the framework of Einstein-Aether theory, with matter content described by a cosmic string fluid and the presence of a negative cosmological constant. The quantization is performed using the minisuperspace formalism with a perfect fluid via the velocity potentials approach, which allows for the interpretation of the fluid-associated variable as an internal time. The resulting Wheeler-DeWitt equation is solved, yielding normalizable eigenstates and associated wave packets. Employing both the many-worlds and the de Broglie-Bohm interpretations, we determine the dynamics of the scale factor and the behavior of the quantum potential. The results demonstrate the absence of singularities in our model, and the independence of the probability density with respect to the spatial curvature.