The Bianchi I model in terms of nonstandard loop quantum cosmology: quantum dynamics

We analyze the quantum Bianchi I model in the setting of nonstandard loop quantum cosmology. Elementary observables are used to quantize the volume operator, and the spectrum of the volume operator is bounded from below and discrete. The discreteness may imply a foamy structure of spacetime at the semiclassical level. The results are described in terms of a free parameter specifying loop geometry to be determined in astro-cosmo observations. An evolution of the quantum model is generated by the so-called true Hamiltonian, which enables the introduction of a time parameter valued in the set of all real numbers.