Drawing conformal diagrams for a fractal landscape

Details Drawing conformal diagrams for a fractal landscape Drawing conformal diagrams for a fractal landscape

2005-03-14

arxiv.org/abs/gr-qc/0503061v1

Phys.Rev.D71:123523,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 25 figures

Scientific paper

10.1103/PhysRevD.71.123523

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.

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