Generalized Einstein-Aether vector field models have been shown to provide, in the weak field regime, modifications to gravity which can be reconciled with the successful modified Newtonian dynamics (MOND) proposal. Very little is known, however, on the function $\mathcal{F}(\mathcal{K})$ defining the vector field Lagrangian so that an analysis of the viability of such theories at the cosmological scales has never been performed. As a first step along this route, we rely on the relation between $\mathcal{F}(\mathcal{K})$ and the MOND interpolating function $\mu (a/a_0)$ to assign the vector field Lagrangian thus obtaining what we refer to as MONDian vector models. Since they are able by construction to recover the MOND successes on galaxy scales, we investigate whether they can also drive the observed accelerated expansion by fitting the models to the type Ia supernovae data. Should this be the case, we have a unified framework where both dark energy and dark matter can be seen as different manifestations of a single vector field. It turns out that both MONDian vector models are able to well fit the low redshift data on type Ia supernovae, while some tension could be present in the high $z$ regime.

• Received 20 May 2009

DOI:https://doi.org/10.1103/PhysRevD.80.063515