Kaluza-Klein bubble like structure and celestial sphere in inflationary universe

TL;DR

This paper explores a five-dimensional deSitter spacetime with a 2-brane, revealing a Kaluza-Klein bubble structure and a celestial sphere, providing insights into the universe's topology and boundary phenomena from a four-dimensional perspective.

Contribution

It introduces a novel five-dimensional deSitter model with a 2-brane, demonstrating a Kaluza-Klein bubble structure and the concept of a celestial sphere in an inflationary universe.

Findings

Spacetime has a bubble-like structure ending at the 2-brane.

The boundary surface acts as a celestial sphere surrounding the spacetime.

Observers see the celestial sphere falling and contact with the 2-brane.

Abstract

We consider five dimensional deSitter spacetimes with a deficit angle due to the presence of a closed 2-brane and identify one dimension as an extra dimension. From the four dimensional viewpoint we can see that the spacetime has a structure similar to a Kaluza-Klein bubble of nothing, that is, four dimensional spacetime ends at the 2-brane. Since a spatial section of the full deSitter spacetime has the topology of a sphere, the boundary surface surrounds the remaining four dimensional spacetime, and can be considered as the celestial sphere. After the spacetime is created from nothing via an instanton which we describe, some four dimensional observers in it see the celestial sphere falling down, and will be in contact with a 2-brane attached on it.