  We investigate the potential for the Deep Underground Neutrino Experiment
(DUNE) to probe the existence and effects of a fourth neutrino mass-eigenstate.
We study the mixing of the fourth mass-eigenstate with the three active
neutrinos of the Standard Model, including the effects of new sources of
CP-invariance violation, for a wide range of new mass-squared differences, from
lower than 10^-5 eV^2 to higher than 1 eV^2. DUNE is sensitive to previously
unexplored regions of the mixing angle - mass-squared difference parameter
space. If there is a fourth neutrino, in some regions of the parameter space,
DUNE is able to measure the new oscillation parameters (some very precisely)
and clearly identify two independent sources of CP-invariance violation.
Finally, we use the hypothesis that there are four neutrino mass-eigenstates in
order to ascertain how well DUNE can test the limits of the
three-massive-neutrinos paradigm. In this way, we briefly explore whether light
sterile neutrinos can serve as proxies for other, in principle unknown,
phenomena that might manifest themselves in long-baseline neutrino oscillation
experiments.
