2005/03/14 by Sergei Winitzki
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.71.123523
published as Phys.Rev.D71:123523,2005 · 14 pages, 25 figures
arxiv created 2005/03/14 · openalex publication_date 2005/06/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Generic models of cosmological inflation and the recently proposed scenarios of a recycling universe and the string theory landscape predict spacetimes whose global geometry is a stochastic, self-similar fractal. To visualize the complicated causal structure of such a universe, one usually draws a conformal (Carter-Penrose) diagram. I develop a new method for drawing conformal diagrams, applicable to arbitrary 1+1-dimensional spacetimes. This method is based on a qualitative analysis of intersecting lightrays and thus avoids the need for explicit transformations of the spacetime metric. To demonstrate the power and simplicity of this method, I present derivations of diagrams for spacetimes of varying complication. I then apply the lightray method to three different models of an eternally inflating universe (scalar-field inflation, recycling universe, and string theory landscape) involving the nucleation of nested asymptotically flat, de Sitter and/or anti-de Sitter bubbles. I show that the resulting diagrams contain a characteristic fractal arrangement of lines.