  The vacuum state in quantum field theory is known to exhibit an important
number of fundamental physical features. In this work we explore the
possibility that this state could also present a non-trivial space-time
structure on large scales. In particular, we will show that by imposing the
renormalized vacuum energy-momentum tensor to be conserved and compatible with
cosmological observations, the vacuum energy of sufficiently heavy fields
behaves at late times as non-relativistic matter rather than as a cosmological
constant. In this limit, the vacuum state supports perturbations whose speed of
sound is negligible and accordingly allows the growth of structures in the
vacuum energy itself. This large-scale structure of vacuum could seed the
formation of galaxies and clusters very much in the same way as cold dark
matter does.
