  Loop quantum cosmology tries to capture the main ideas of loop quantum
gravity and to apply them to the Universe as a whole. Two main approaches
within this framework have been considered to date for the study of
cosmological perturbations: the dressed metric approach and the deformed
algebra approach. They both have advantages and drawbacks. In this article, we
accurately compare their predictions. In particular, we compute the associated
primordial tensor power spectra. We show -- numerically and analytically --
that the large scale behavior is similar for both approaches and compatible
with the usual prediction of general relativity. The small scale behavior is,
the other way round, drastically different. Most importantly, we show that in a
range of wavenumbers explicitly calculated, both approaches do agree on
predictions that, in addition, differ from standard general relativity and do
not depend on unknown parameters. These features of the power spectrum at
intermediate scales might constitute a universal loop quantum cosmology
prediction that can hopefully lead to observational tests and constraints. We
also present a complete analytical study of the background evolution for the
bouncing universe that can be used for other purposes.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory