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Bubble fluctuations in Omega less than 1 inflation
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In the context of the open inflationary universe, we calculate the amplitude of quantum fluctuations which deform the bubble shape. These give rise to scalar field fluctuations in the open Friedmann-Robertson-Walker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the perturbations behave as tensor modes (gravitational waves of very long wave-length). For
(
1
−
Ω
)
≪
1
, where
Ω
is the density parameter, the microwave temperature anisotropies produced by these modes are of order
δ
T
T
∼
H
(
R
0
μ
l
)
−
1
2
(
1
−
Ω
)
l
2
. Here,
H
is the expansion rate during inflation,
R
0
is the intrinsic radius of the bubble at the time of nucleation,
μ
is the bubble wall tension, and
l
labels the different multipoles (
l
>
1
). The gravitational back reaction of the bubble has been ignored. In this approximation,
G
μ
R
0
≪
1
, and the new effect can be much larger than the one due to ordinary gravitational waves generated during inflation (unless, of course,
Ω
gets too close to 1, in which case the new effect disappears).
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GARRIGA TORRES, Jaume. Bubble fluctuations in Omega less than 1 inflation. Physical Review D. 1996. Vol. 54, num. 8, pags. 4764-4769. ISSN 0556-2821. [consulted: 3 of July of 2026]. Available at: https://hdl.handle.net/2445/12336