Revisiting the Origin of the Universe and the Arrow of Time

TL;DR

The paper tackles the origin of the universe and the arrow of time by arguing that a closed FRW universe can be free of singularities through a no-boundary/tunneling picture, with the Wheeler-DeWitt equation $\mathcal{H}\Psi=0$ yielding an intrinsic, locally defined dynamical time. Focusing on a two-dimensional Jackiw-Teitelboim gravity setup, it derives local time variables $\sigma_\pm$ and shows the dynamical time, together with a cosmological time associated with expansion, aligns with the thermodynamic arrow of time—constructed via quantum decoherence of the density matrix and showing a symmetric behavior about the maximal scale factor $a_{max}$. The explicit 2D solution demonstrates how a contracting phase can be described with a consistent time direction, potentially avoiding global time-path inconsistencies. The discussion touches on extensions to four dimensions and related frameworks (AB time, Penrose CCC, AdS/CFT), outlining a path to connect quantum cosmology with entropy flow and the cosmological arrow of time.

Abstract

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.

Figures (3)

• Figure 1: The birth of the inflating universe from nothing Vilenkin, which is possible only in the closed universe. The horizontal axis is the FRW scale factor $a$ and the vertical axis is $U(a,\phi)$ given in (\ref{['closed']}). In the open universe, $U(a,\phi)$ is obtained by changing the signature of $H^2a^2$ in (\ref{['closed']}) and has no barrier to the singular point $a=0$.
• Figure 2: Classical trajectory in the $\sigma_--\sigma_+$Kamimura2. $B$ is the point at the maximal scale $a_{max}$. At the point $A$ and further, the condition $\dot{\sigma}_->0$ is broken.
• Figure 3: Quantum coherence width $\sigma^2$ versus the scale factor $a$ is shown for the closed universe Morikawa. $A$ and $B$ points correspond to those of Fig.2.