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.

We study the fermionic Schwinger effect in two dimensional de Sitter spacetime. To do so we first present a method to semiclassically compute the number of pairs created per momentum mode for general time dependent fields. In addition the constant electric field is studied in depth. In this case solutions for the Dirac equation can be found and the number of pairs can be computed using the standard Bogoliubov method. This result is shown to agree with the semiclassical one in the appropriate limit. The solutions are also used to compute the expectation value of the induced current. Comparing these results to similar studies for bosons we find that while the results agree in the semiclassical limit they do not generally. Especially there is no occurrence of a strong current for small electric fields.Comment: 19 pages, 1 figure, V2:small changes and some references added, version accepted for publication in Phys. Rev.