Euclidian Vacuum Mode Functions for a Scalar Field on Open De Sitter Spacetime

TL;DR

This paper derives explicit Euclidean vacuum mode functions for a scalar field in open de Sitter spacetime, relevant for understanding quantum fluctuations in open inflationary universe models.

Contribution

It provides the first explicit expressions for Euclidean vacuum mode functions in an open de Sitter chart for arbitrary scalar mass and curvature coupling.

Findings

Explicit mode functions for scalar fields in open de Sitter space.

Applicable to models of open inflation with initial Euclidean vacuum.

Facilitates analysis of quantum fluctuations in open universe scenarios.

Abstract

Motivated by recent studies of the one-bubble inflationary universe scenario that predicts a low density, negative curvature universe, we investigate the Euclidean vacuum mode functions of a scalar field in a spatially open chart of de Sitter space which is foliated by hyperbolic time slices. When we consider the possibility of an open inflationary universe, we are faced with the problem of the initial condition for the quantum fluctuations of the inflaton field, because the inflationary era should not last too long to lose every information of the initial condition. In the one-bubble scenario in which an open universe is created in an exponentially expanding false vacuum universe triggered by quantum decay of false vacuum, it seems natural that the initial state is the de Sitter-invariant Euclidean vacuum. Here we present explicit expressions for the Euclidean vacuum mode functions in the open chart for a scalar field with arbitrary mass and curvature coupling.