Asymptotic silence in loop quantum cosmology
  The state of asymptotic silence, characterized by causal disconnection of the
space points, emerges from various approaches aiming to describe gravitational
phenomena in the limit of large curvatures. In particular, such behavior was
anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous
conjecture put forward in the early seventies of the last century. While the
BKL conjecture is based on purely classical considerations, one can expect that
asymptotic silence should have its quantum counterpart at the level of a more
fundamental theory of quantum gravity, which is the relevant description of
gravitational phenomena in the limit of large energy densities. Here, we
summarize some recent results which give support to such a possibility. More
precisely, we discuss occurrence of the asymptotic silence due to
polymerization of space at the Planck scale, in the framework of loop quantum
cosmology. In the discussed model, the state of asymptotic silence is realized
at the energy density $\rho = \rho_c/2$, where $\rho_c$ is the maximal allowed
energy density, being of the order of the Planck energy density. At energy
densities $\rho > \rho_c/2$, the universe becomes 4D Euclidean space without
causal structure. Therefore, the asymptotic silence appears to be an
intermediate state of space between the Lorentzian and Euclidean phases.
