The Einstein-Elko system -- Can dark matter drive inflation?

Recently, a spin one half matter field with mass dimension one was discovered, called Elko spinors. The present work shows how to introduce these fields into a curved spacetime by the standard covariantisation scheme. After formulating the coupled Einstein-Elko field equations, the spacetime is assumed to be homogeneous and isotropic in order to simplify the resulting field equations. Analytical ghost Elko solutions are constructed which have vanishing energy-momentum tensor without and with cosmological constant. The cosmological Elko theory is finally related to the standard scalar field theory with self interaction that gives rise to inflation and it is pointed out that the Elko spinors are not only prime dark matter candidates but also prime candidates for inflation.