Oscillating Quintom Model with Time Periodic Varying Deceleration Parameter

We propose a new law for the deceleration parameter that varies periodically with time. According to the law, we give a model of the oscillating universe with quintom matter in the framework of a 4-dimensional Friedmann–Robertson–Walker background. We find that, in the model, the Hubble parameter oscillates and keeps positive. The universe undergoes decelerating expansion and accelerating expansion alternately without singularity.