  Recently, the possibility of a low-temperature non-cubic phase in BaZrO$_3$
has generated engaging discussions about its true ground state and the
consequences on its physical properties. In this paper, we investigate the
microscopic behavior of the BaZrO$_3$ cubic phase by developing a shell model
from $ab~initio$ calculations and by performing molecular dynamics simulations
at finite temperature and under negative pressure. We study three different
scenarios created by tuning the intensities of the antiferrodistortive (AFD)
instabilities, and consequently, the sequence of phase transitions with
temperature. From a detailed analysis of the cubic phase at atomic scale, we
find that oxygen octahedra are barely distorted, present rotation angles that
may oscillate with significant amplitudes, are AFD correlated with their
closest neighbors on the plane perpendicular to the pseudocubic rotation axis
exhibiting $(0 0 a^-)$-type ordering, and form instantaneous, dynamic and
unstable domains over time. Our simulations support the existence of
nanoregions with short-range ordering in cubic BaZrO$_3$ associated with
experimentally observed anomalies and unveil that they can exist regardless of
whether or not structural phase transitions related with AFD distortions occur
at lower temperatures.
