In this paper, the cosmological dynamics of Brans-Dicke (BD) theory in which there are fermions with a coupling to BD scalar field as well as a self-interaction potential is investigated. The conditions that there exists a solution which is stable and represents a late-time accelerated expansion of the Universe are found. The variable mass of fermions cannot vanish exactly during the evolution of the Universe once it exists initially. It is shown that the late-time acceleration depends completely on the self-interaction of the fermion field if our investigation is restricted to the theory with positive BD parameter $\omega$. Provided a negative $\omega$ is allowed, there will be another two classes of stable solutions describing the late-time accelerated expansion of the Universe.

• Received 30 May 2010

DOI:https://doi.org/10.1103/PhysRevD.82.063523