Can hyperbolic phase of Brans-Dicke field account for Dark Matter?
  We show that the introduction of a hyperbolic phase for Brans-Dicke (BD) field results in a flat vacuum cosmological solution of Hubble parameter H and fractional rate of change of BD scalar field, F which asymptotically approach constant values. At late stages, hyperbolic phase of BD field behaves like dark matter. 
M. Arik, M. Calik and F. Cifter