It has been suggested recently that the change in cosmological redshift (the Sandage test of expansion) could be observed in the next generation of large telescopes and ultra-stable spectrographs. In a recent paper we estimated the change of peculiar
velocity, i.e. the peculiar acceleration, in nearby galaxies and clusters and shown it to be of the same order of magnitude as the typical cosmological signal. Mapping the acceleration field allows for a reconstruction of the galactic gravitational potential without assuming virialization. In this paper we focus on the peculiar acceleration in our own Galaxy, modeled as a Kuzmin disc and a dark matter spherical halo. We estimate the peculiar acceleration for all known Galactic globular clusters and find some cases with an expected velocity shift in excess of 20 cm/sec for observations fifteen years apart, well above the typical cosmological acceleration. We then compare the predicted signal for a MOND (modified Newtonian dynamics) model in which the spherical dark matter halo is absent. We find that the signal pattern is qualitatively different, showing that the peculiar acceleration field could be employed to test competing theories of gravity. However the difference seems too small to be detectable in the near future.
We explore the dynamics of cosmological models with two coupled dark components with energy densities $rho_A$ and $rho_B$. We assume that the coupling is of the form $Q=Hq(rho_A,rho_B)$, so that the dynamics of the two components turns out to be scal
e independent, i.e. does not depend explicitly on the Hubble scalar $H$. With this assumption, we focus on the general linear coupling $q=q_o+q_Arho_A+q_Brho_B$, which may be seen as arising from any $q(rho_A,rho_B)$ at late time and leads in general to an effective cosmological constant. In the second part of the paper we consider observational constraints on the form of the coupling from SN Ia data, assuming that one of the components is cold dark matter. We find that the constant part of the coupling function is unconstrained by SN Ia data and, among typical linear coupling functions, the one proportional to the dark energy density $rho_{A}$ is preferred in the strong coupling regime, $|q_{A}|>1$. While phantom models favor a positive coupling function, in non-phantom models, not only a negative coupling function is allowed, but the uncoupled sub-case falls at the border of the likelihood.
