Abstract
It is argued that the observed thermodynamic arrow of time must arise from the boundary conditions of the Universe. We analyze the consequences of the no-boundary proposal, the only reasonably complete set of boundary conditions that has been put forward. We study perturbations of a Friedmann model containing a massive scalar field, but our results should be independent of the details of the matter content. We find that gravitational wave perturbations have an amplitude that remains in the linear regime at all times and is roughly time symmetric about the time of maximum expansion. Thus gravitational wave perturbations do not give rise to an arrow of time. However, density perturbations behave very differently. They are small at one end of the Universe's history, but grow larger and become nonlinear as the Universe gets larger. Contrary to an earlier claim, the density perturbations do not get small again at the other end of the Universe's history. They therefore give rise to a thermodynamic arrow of time that points in a constant direction while the Universe expands and contracts again. The arrow of time does not reverse at the point of maximum expansion. One has to appeal to the weak anthropic principle to explain why we observe the thermodynamic arrow to agree with the cosmological arrow, the direction of time in which the Universe is expanding.
- Received 18 December 1992
DOI:https://doi.org/10.1103/PhysRevD.47.5342
©1993 American Physical Society
Collections
This article appears in the following collection:
The Work of Stephen Hawking in Physical Review
To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."
