Arrow of time in string theory
Brett McInnesa,
aNational University of Singapore, Singapore
Received 24 November 2006; revised 24 April 2007; accepted 7 May 2007. Available online 16 May 2007.
Abstract
Inflation allows the problem of the arrow of time to be understood as a question about the structure of spacetime: why was the intrinsic curvature of the earliest spatial sections so much better behaved than it might have been? This is really just the complement of a more familiar problem: what mechanism prevents the extrinsic curvature of the earliest spatial sections from diverging, as classical general relativity suggests? We argue that the stringy version of “creation from nothingâ€, sketched by Ooguri, Vafa, and Verlinde, solves both of these problems at once. The argument, while very simple, hinges on some of the deepest theorems in global differential geometry. These results imply that when a spatially toral spacetime is created from nothing, the earliest spatial sections are forced to be [quasi-classically] exactly locally isotropic. This local isotropy, in turn, forces the inflaton into its minimal-entropy state. The theory explains why the arrow does not reverse in black holes or in a cosmic contraction, if any.
Nuclear Physics B
Volume 782, Issues 1-2, 15 October 2007, Pages 1-25