  We present an analysis of the pairwise velocity statistics from a suite of
cosmological N-body simulations describing the "Running
Friedmann-Lema\^itre-Robertson-Walker" (R-FLRW) cosmological model. This model
is based on quantum field theory in a curved space-time and extends
{\Lambda}CDM with a time-evolving vacuum energy density. To enforce local
conservation of matter a time-evolving gravitational coupling is also included.
Our results constitute the first study of velocities in the R-FLRW cosmology,
and we also compare with other dark energy simulations suites, repeating the
same analysis. We find a strong degeneracy between the pairwise velocity and
{\sigma}_8 at z=0 for almost all scenarios considered, which remains even when
we look back to epochs as early as z=2. We also investigate various Coupled
Dark Energy models, some of which show minimal degeneracy, and reveal
interesting deviations from {\Lambda}CDM which could be readily exploited by
future cosmological observations to test and further constrain our
understanding of dark energy.
