2006/11/30 by Brett McInnes
Mathematics · Physics and Astronomy · #Arrow #Arrow of time #Black Holes and Theoretical Physics #Classical mechanics #Cosmic censorship hypothesis #Cosmology and Gravitation Theories #Curvature #Differential geometry #Entropy (arrow of time) #General relativity #Geometry #Mathematics #Nothing #Philosophy #Physics #Quantum #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #String theory #Theoretical physics #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2007.05.005
published as Nucl.Phys.B782:1-25,2007 · 30 pages, one diagram, various clarifications, references updated, version to appear in Nuclear Physics B
arxiv created 2007/05/09 · openalex publication_date 2007/05/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 nothing", 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.