  We introduce an extension of the Born-Infeld action for a scalar field and
show that it can act as unifying-dark-matter, providing an explanation for both
structure formation and the accelerated expansion of the universe. We
investigate the cosmological dynamics of this theory in a particular case,
referred as the "Milne-Born-Infeld" (MBI) Lagrangian. We show that this model,
whose equation of state has effectively a single free parameter, is consistent
with recent type Ia supernovae data, providing a fit as good as for the
$\Lambda$CDM model with the same number of degrees of freedom. Furthermore,
this parameter is tightly constrained by current data, making the model easily
testable with other observables. Contrary to previous candidates for
unifying-dark-matter, the sound velocity of the MBI model is vanishing both
close to the dark matter state as well as near the cosmological constant state.
This could avoid the problems on the matter power spectrum that were present in
previous adiabatic dark-matter/dark-energy unification models. We also present
a short discussion on the causal propagation in nonlinear scalar field theories
such as the one proposed here.
