Revisiting the Origin of the Universe and the Arrow of Time

We reconsider the old but yet unsolved problems, origin of the universe and the arrow of time. We show that only the closed universe is free from the singularity with the arrow of time symmetric with respect to the maximal size of the cosmic scale. The Wheeler-DeWitt equation is explicitly solved to obtain the local dynamical times. Corresponding to these local dynamical times, the thermodynamic arrow of time is proved to coincide with the arrows of dynamical time and of expanding universe (cosmological time). The proof is explicitly shown in two-dimensional spacetime.