Global Spacetime Structure of Compactified Inflationary Universe

Understand

We investigate the global spacetime structure of torus de Sitter universe, which is exact de Sitter space with torus identification based on the flat chart.

• We show that past incomplete null geodesics in torus de Sitter universe are locally extendible.
• Then we give an extension of torus de Sitter universe so that at least one of the past incomplete null geodesics in the original spacetime becomes complete.
• However we find that extended torus de Sitter universe has two ill behaviors.