The Stephani Universe, k-essence and strings in the 5-th dimension

The Stephani universe is an inhomogeneous alternative to $\Lambda{\rm CDM}$ .We show that the exotic fluid driving the Stephani exact solution of Einstein's equations is an unusual form of k-essence that is linear in "velocity". Much as the Stephani universe can be embedded into (a section of) flat 5-d Minkowski space-time, we show that the k-essence obtains through dimensional reduction of a 5-d strongly coupled non-linear "electrodynamics" that, in the empty Stephani universe, is similar to the Nielsen-Olesen field theory of the dual string.