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Loop quantum cosmology tries to capture the main ideas of loop quantumgravity and to apply them to the Universe as a whole. Two main approacheswithin this framework have been considered to date for the study ofcosmological perturbations: the dressed metric approach and the deformedalgebra approach. They both have advantages and drawbacks. In this article, weaccurately compare their predictions. In particular, we compute the associatedprimordial tensor power spectra. We show -- numerically and analytically --that the large scale behavior is similar for both approaches and compatiblewith the usual prediction of general relativity. The small scale behavior is,the other way round, drastically different. Most importantly, we show that in arange of wavenumbers explicitly calculated, both approaches do agree onpredictions that, in addition, differ from standard general relativity and donot depend on unknown parameters. These features of the power spectrum atintermediate scales might constitute a universal loop quantum cosmologyprediction that can hopefully lead to observational tests and constraints. Wealso present a complete analytical study of the background evolution for thebouncing universe that can be used for other purposes.

Comparison of primordial tensor power spectra from the deformed algebra and dressed metric approaches in loop quantum cosmology