  General Relativity predicts that the spacetime near a cosmological
singularity undergoes an infinite number of chaotic oscillations between
different Kasner epochs with rapid transitions between them. This so-called BKL
behaviour persists in the presence of several types of classical matter. Little
is known in the presence of quantum effects. A major obstacle is the fact that
the fast metric oscillations inevitably drive the matter far from equilibrium.
We use holography to determine the evolution of the quantum stress tensor of a
non-conformal, strongly-coupled, four-dimensional gauge theory in a Kasner
spacetime. The stress tensor near the singularity is solely controlled by the
ultraviolet fixed point of the gauge theory, and it diverges in a universal way
common to all theories with a gravity dual. We then compute the backreaction of
the stress tensor on the Kasner metric to leading order in the gravitational
coupling. The modification of the Kasner exponents that we find suggests that
the BKL behaviour may be avoided in the presence of quantum matter.
