States of low energy in bouncing inflationary scenarios in loop quantum cosmology
Mercedes Martín-Benito, Rita B. Neves, Javier Olmedo
Abstract
In generic Friedmann-Lema\^{\i}tre-Robertson-Walker spacetimes, states of low energy (SLEs) are defined to minimize the regularized energy density smeared along the timelike curve of an isotropic observer, which is specified via a smearing function. For every smearing function, SLEs are unique (up to a phase) and are shown to be exact Hadamard states. In this work, we investigate the viability of SLEs as the vacuum for cosmological perturbations in hybrid loop quantum cosmology, motivated by the fact that SLEs have been shown to provide suitable vacua in models where a period of kinetic dominance precedes inflation. We find that there are two classes of smearing functions that can be seen as natural choices within this context, for which the corresponding SLEs and the resulting power spectra at the end of inflation are quite insensitive to the exact shape and support of the smearing function. Furthermore, a preliminary analysis of the tensor-to-scalar ratio and of the spectral index indicates as good an agreement with observations as that of standard cosmology.