The time-dependent mass of cosmological perturbations in loop quantum cosmology: Dapor-Liegener regularization

35 pags., 5 figs.
In this work, we compute the time-dependent masses that govern the dynamics of scalar and tensor perturbations propagating on an effective flat, homogeneous, and isotropic background within the framework of loop quantum cosmology (LQC), regularized according to the procedure put forward by Dapor and Liegener. To do so, we follow the two main approaches that, in the field of LQC, lead to hyperbolic equations for the perturbations in the ultraviolet sector: the hybrid and dressed metric formalisms. This allows us to compare the masses resulting from both proposals and analyze their positivity in regimes of physical interest: the big bounce and the contracting de Sitter phase in the asymptotic past that is a defining feature of the model under consideration.
This work has been supported by Project No. FIS2017-86497-C2-2-P of MICINN from Spain. A GarciaQuismondo acknowledges that the project that gave rise to these results received the support of a fellowship from ‘la Caixa’ Foundation (ID 100010434). The fellowship code is LCF/BQ/DR19/11740028. G Sanchez Perez acknowledges support of the Grant No. CSIC JAEINT19_EX_0632.