  We explore the effects of non-standard neutrino interactions (NSI) and how
they modify neutrino propagation in the Deep Underground Neutrino Experiment
(DUNE). We find that NSI can significantly modify the data to be collected by
the DUNE experiment as long as the new physics parameters are large enough. For
example, If the DUNE data are consistent with the standard
three-massive-neutrinos paradigm, order 0.1 (in units of the Fermi constant)
NSI effects will be ruled out. On the other hand, if large NSI effects are
present, DUNE will be able to not only rule out the standard paradigm but also
measure the new physics parameters, sometimes with good precision. We find
that, in some cases, DUNE is sensitive to new sources of CP-invariance
violation. We also explored whether DUNE data can be used to distinguish
different types of new physics beyond nonzero neutrino masses. In more detail,
we asked whether NSI can be mimicked, as far as the DUNE setup is concerned, by
the hypothesis that there is a new light neutrino state.
