The eternal rainbow universe

There are many strong theoretical motivations on why there can be a Lorentz invariance violation due to quantum gravity effects at length scales of the order of Planck length. In this present study, we consider some theoretical arguments which either favors the idea of Lorentz invariance violation or modifies the action of the Lorentz group acting on momentum space. All these ideas predicts a modification in the dispersion relation that depends on some functions known as Rainbow functions. With simple calculations and arguments we show that there are some unique choices of the Rainbow functions which predict an infinitely existing universe near the Plank scale and hence resolve the big bang singularity.