Can MONDian vector theories explain the cosmic speed up ?

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 successfull MOND proposal. Very little is known, however, on the function F(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 F(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 be this 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.Comment: 15 pages, 5 tables, 4 figures, accepted for publication on Physical Review

The MOND Fundamental Plane

Modified Newtonian Dynamics (MOND) has been shown to be able to fit spiral galaxy rotation curves as well as giving a theoretical foundation for empirically determined scaling relations, such as the Tully - Fisher law, without the need for a dark matter halo. As a complementary analysis, one should investigate whether MOND can also reproduce the dynamics of early - type galaxies (ETGs) without dark matter. As a first step, we here show that MOND can indeed fit the observed central velocity dispersion $\sigma_0$ of a large sample of ETGs assuming a simple MOND interpolating functions and constant anisotropy. We also show that, under some assumptions on the luminosity dependence of the Sersic n parameter and the stellar M/L ratio, MOND predicts a fundamental plane for ETGs : a log - linear relation among the effective radius $R_{eff}$, $\sigma_0$ and the mean effective intensity $\langle I_e \rangle$. However, we predict a tilt between the observed and the MOND fundamental planes.Comment: 16 pages, 2 figures, 2 tables, accepted for publication on MNRA