  Dual-helicity eigenspinors of the charge conjugation operator (ELKO spinor
fields) belong -- together with Majorana spinor fields -- to a wider class of
spinor fields, the so-called flagpole spinor fields, corresponding to the
class-(5), according to Lounesto spinor field classification based on the
relations and values taken by their associated bilinear covariants. There
exists only six such disjoint classes: the first three corresponding to Dirac
spinor fields, and the other three respectively corresponding to flagpole,
flag-dipole and Weyl spinor fields. Using the mapping from ELKO spinor fields
to the three classes Dirac spinor fields, it is shown that the
Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived
from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for
supergravity. The Holst action is related to the Ashtekar's quantum gravity
formulation. To each one of these classes, there corresponds a unique kind of
action for a covariant gravity theory. Furthermore we consider the necessary
and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order
to naturally extend the Standard Model to spinor fields possessing mass
dimension one. As ELKO is a prime candidate to describe dark matter and can be
obtained from the DSFs, via a mapping explicitly constructed that does not
preserve spinor field classes, we prove that in particular the
Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the
QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The
geometric meaning of the mass dimension-transmuting operator - leading ELKO
Lagrangian into the Dirac Lagrangian - is also pointed out, together with its
relationship to the instanton Hopf fibration.
