Following the approach of the induced-matter theory, we investigate the cosmological implications of a five-dimensional Brans-Dicke theory, and propose to explain the acceleration of the universe. After inducing in a four-dimensional hypersurface, we classify the energy-momentum tensor into two parts in a way that, one part represents all kind of the matter (the baryonic and dark) and the other one contains every extra terms emerging from the scale factor of the fifth dimension and the scalar field, which we consider as the energy-momentum tensor of dark energy. We also separate the energy-momentum conservation equation into two conservation equations, one for matter and the other for dark energy. We perform this procedure for different cases, without interacting term and with two particular (suitable) interacting terms between the two parts. By assuming the parameter of the state equation for dark energy to be constant, the equations of the model admit the power-law solutions. Though, the non-interacting case does not give any accelerated universe, but the interacting cases give both decelerated and accelerated universes. For the interacting cases, we figure out analytically the acceptable ranges of some parameters of the model, and also investigate the data analysis to test the model parameter values consistency with the observational data of the distance modulus of 580 SNe Ia compiled in Union2.1. For one of these interacting cases, the best fitted values suggest that the Brans-Dicke coupling constant (ω) is ≃ −7.75, however, it also gives the state parameter of dark energy (w X ) equal to ≃ −0.67. In addition, the model gives the Hubble and deceleration parameters at the present time to be H • ≃ 69.4 (km/s)/Mpc and q • ≃ −0.38 (within their confidence intervals), where the scale factor of the fifth dimension shrinks with the time.

Shell galaxies are understood to form through the collision of a dwarf galaxy with an elliptical galaxy. Shell structures and kinematics have been noted to be independent tools to measure the gravitational potential of the shell galaxies. We compare theoretically the formation of shells in Type I shell galaxies in different gravity theories in this work because this is so far missing in the literature. We include Newtonian plus dark halo gravity, and two non-Newtonian gravity models, MOG and MOND, in identical initial systems. We investigate the effect of dynamical friction, which by slowing down the dwarf galaxy in the dark halo models limits the range of shell radii to low values. Under the same initial conditions, shells appear on a shorter timescale and over a smaller range of distances in the presence of dark matter than in the corresponding non-Newtonian gravity models. If galaxies are embedded in a dark matter halo, then the merging time may be too rapid to allow multi-generation shell formation as required by observed systems because of the large dynamical friction effect. Starting from the same initial state, in the dark halo model the observation of small bright shells should be accompanied by large faint ones, while for the case of MOG, the next shell generation patterns iterate with a specific time delay. The first shell generation pattern shows a degeneracy with the age of the shells and in different theories, but the relative distance of the shells and the shell expansion velocity can break this degeneracy.