  We investigate the primordial power spectrum of cosmological tensor
perturbations in the dressed metric approach to Loop Quantum Cosmology. We
compute the background-dependent effective mass that affects their propagation
using the effective description of Loop Quantum Cosmology and show that this
mass can be approximated in different cosmological epochs by appropriate
analytic functions. Moreover, in each of those epochs we can analytically solve
the propagation of the perturbations, then obtaining the general solution
globally by continuity requirements. On the other hand, since there are regimes
far away from slow roll in the considered background evolution, the
Bunch-Davies state does not provide a privileged choice of vacuum that would
pick out a specific solution for the perturbations. Instead, we select the
state of these perturbations by a recently proposed criterion that removes
unwanted oscillations in the power spectrum. We compute the spectrum of this
vacuum and compare it with other spectra obtained in the literature, especially
with one corresponding to the hybrid approach to Loop Quantum Cosmology.
Finally, we notice that the same type of background dynamics is found in a
phenomenological approach to quantum gravity based on thermodynamics, allowing
in this case a free value for the tantamount of the critical density. Extending
the dressed metric proposal to this phenomenological model, one might expect a
similar form for the associated primordial power spectrum.
