Singularity avoidance, clocks and primordial power spectrum

There are ways to cure the singularity problem in cosmology
by means of quantum effects. In the process, one encounters
the question of time, which can for instance be addressed by
using an internal degree of freedom. Applying such a method
to an anisotropic Bianchi I model where the shear serves as a
clock, I show that some generic features can be obtained for
the trajectory of the average scale factor, all avoiding the
singularity and reaching similar asymptotic states, deemed
semi-classical. Using a trajectory approach yields similar
conclusions, with the intriguing possibility to modify the
primordial power spectrum of cosmological perturbations
on the largest scales.