Oscillating universe in the DGP braneworld

With a method in which the Friedmann equation is written in a form such that evolution of the scale factor can be treated as that of a particle in a "potential", we classify all possible cosmic evolutions in the DGP braneworld scenario with the dark radiation term retained. By assuming that the energy component is pressureless matter, radiation or vacuum energy, respectively, we find that in the matter or vacuum energy dominated case, the scale factor has a minimum value $a_0$. In the matter dominated case, the big bang singularity can be avoided in some special circumstances, and there may exist an oscillating universe or a bouncing one. If the cosmic scale factor is in the oscillating region initially, the universe may undergo an oscillation. After a number of oscillations, it may evolve to the bounce point through quantum tunneling and then expand. However, if the universe contracts initially from an infinite scale, it can turn around and then expand forever. In the vacuum energy dominated case, there exists a stable Einstein static state to avoid the big bang singularity. However, in certain circumstances in the matter or vacuum energy dominated case, a new kind of singularity may occur at $a_0$ as a result of the discontinuity of the scale factor. In the radiation dominated case, the universe may originate from the big bang singularity, but a bouncing universe which avoids this singularity is also possible.