There was a model claiming the birth of the universe from nothing, but the specific mechanism for the birth and expansion of the universe was very poor. According to the energy-time uncertainty principle, during Δt, an energy fluctuation of ΔE is possible, but this energy fluctuation should have reverted back to nothing. By the way, there is also a gravitational interaction during the time of Δt, and if the negative gravitational self-energy exceeds the positive mass-energy during this Δt, the total energy of the corresponding mass distribution becomes negative energy, that is, the negative mass state. Because there is a repulsive gravitational effect between negative masses, this mass distribution expands. Thus, it is possible to create an expansion that does not go back to nothing. Calculations show that if the quantum fluctuation occur for a time less than Δt=(3/10)^(1/2)t_p ~ 0.77t_p, then an energy fluctuation of ΔE > (5/6)^(1/2)m_pc^2 ~ 0.65m_pc^2 must occur. But in this case, because of the negative gravitational self-energy, ΔE will enter the negative energy (mass) state before the time of Δt. Because there is a repulsive gravitational effect between negative masses, ΔE cannot contract, but expands. Thus, the universe does not return to nothing, but can exist. Gravitational Potential Energy Model provides a means of distinguishing whether the existence of the present universe is an inevitable event or an event with a very low probability. And, it presents a new model for the process of inflation, the accelerating expansion of the early universe. This paper also provides an explanation for why the early universe started in a dense state and solves the vacuum catastrophe problem. Additionally, when the negative gravitational potential energy exceeds the positive energy, it can produce an accelerated expansion of the universe. Through this mechanism, inflation, which is the accelerated expansion of the early universe, and dark energy, which is the cause of the accelerated expansion of the recent universe, can be explained at the same time.