Maximal extensions and singularities in inflationary spacetimes

Understand

Extendibility of inflationary spacetimes with flat spatial geometry is investigated.

• We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio $\dot{H}/a^2$ diverges at the boundary, where $\dot{H}$ and $a$ represent the time derivative of the Hubble parameter and the scale factor, respectively.
• On the other hand, if the ratio $\dot{H}/a^2$ converges, then the past boundary is regular and continuously extendible.
• We also develop a method to judge the continuous ($C^0$)extendibility of spacetime in the case of slow-roll inflation driven by a canonical scalar field.