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Metric Perturbations from Quantum Tunneling in Open Inflation
Astrophysics · Submitted 5 Oct 1995
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting bounds on the amplitude of quantum fluctuations of the bubble wall from the absence of such an effect in the observed microwave background anisotropies are quite strong.
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The abstract, sentence by sentence
We study the effect that quantum fluctuations produced during the nucleation of a single-bubble open inflationary universe have on the amplitude of temperature anisotropies in the microwave background. We compute the instanton action for the quantum tunneling between the false and true vacua in open inflation models and show that the amplitude of quantum fluctuations of the bubble wall is very sensitive to the gravitational effects of the true vacuum. We study the spectrum of quantum fluctuations of the bubble wall and confirm that there is only an inhomogeneous ($k^2 = -3$) discrete mode associated with transverse traceless fluctuations of the bubble wall. This super-curvature mode could in principle distort the anisotropy of the microwave background. We compute the amplitude of the gauge invariant metric perturbations induced by the bubble wall fluctuations on a comoving hypersurface, and calculate the induced amplitude of temperature fluctuations in the microwave background, for arbitrary values of $\Omega_0$. We find that in the limit $\Omega_0\simeq 1$, the quadrupole dominates the angular power spectrum, like in the usual Grishchuk-Zel'dovich effect. The resulting bounds on the amplitude of quantum fluctuations of the bubble wall from the absence of such an effect in the observed microwave background anisotropies are quite strong. We also study the contribution from a discrete long wavelength super-curvature mode ($k^2 \simeq 2m^2/3H^2$) that appears in the spectrum of open de Sitter vacuum fluctuations. We constrain the parameters of the models of open inflation so that these modes do not distort the observed temperature anisotropy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the effect that quantum fluctuations produced during the nucleation of a single-bubble open inflationary universe have on the amplitude of temperature anisotropies in the microwave background. | contribution 0.92 | 0.85 | 0.05 | asserted 0.54 |
| s1 | We compute the instanton action for the quantum tunneling between the false and true vacua in open inflation models and show that the amplitude of quantum fluctuations of the bubble wall is very sensitive to the gravitational effects of the true vacuum. | result 0.55 | 0.96 | 0.11 | asserted 1.00 |
| s2 | We study the spectrum of quantum fluctuations of the bubble wall and confirm that there is only an inhomogeneous ($k^2 = -3$) discrete mode associated with transverse traceless fluctuations of the bubble wall. | result 0.86 | 0.95 | 0.08 | asserted 1.00 |
| s3 | This super-curvature mode could in principle distort the anisotropy of the microwave background. | interpretation 0.92 | 0.21 | 0.06 | hedged possibility 1.00 |
| s4 | We compute the amplitude of the gauge invariant metric perturbations induced by the bubble wall fluctuations on a comoving hypersurface, and calculate the induced amplitude of temperature fluctuations in the microwave background, for arbitrary values of $\Omega_0$. | method 0.53 | 0.97 | 0.08 | asserted 0.99 |
| s5 | We find that in the limit $\Omega_0\simeq 1$, the quadrupole dominates the angular power spectrum, like in the usual Grishchuk-Zel'dovich effect. | result 0.99 | 0.95 | 0.12 | asserted 1.00 |
| s6 | The resulting bounds on the amplitude of quantum fluctuations of the bubble wall from the absence of such an effect in the observed microwave background anisotropies are quite strong. | result 0.68 | 0.91 | 0.55 | asserted 1.00 |
| s7 | We also study the contribution from a discrete long wavelength super-curvature mode ($k^2 \simeq 2m^2/3H^2$) that appears in the spectrum of open de Sitter vacuum fluctuations. | contribution 0.99 | 0.77 | 0.05 | asserted 0.97 |
| s8 | We constrain the parameters of the models of open inflation so that these modes do not distort the observed temperature anisotropy. | result 0.71 | 0.94 | 0.31 | asserted 0.97 |
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Original abstract
We study the effect that quantum fluctuations produced during the nucleation of a single-bubble open inflationary universe have on the amplitude of temperature anisotropies in the microwave background. We compute the instanton action for the quantum tunneling between the false and true vacua in open inflation models and show that the amplitude of quantum fluctuations of the bubble wall is very sensitive to the gravitational effects of the true vacuum. We study the spectrum of quantum fluctuations of the bubble wall and confirm that there is only an inhomogeneous ($k^2 = -3$) discrete mode associated with transverse traceless fluctuations of the bubble wall. This super-curvature mode could in principle distort the anisotropy of the microwave background. We compute the amplitude of the gauge invariant metric perturbations induced by the bubble wall fluctuations on a comoving hypersurface, and calculate the induced amplitude of temperature fluctuations in the microwave background, for arbitrary values of $\Omega_0$. We find that in the limit $\Omega_0\simeq 1$, the quadrupole dominates the angular power spectrum, like in the usual Grishchuk-Zel'dovich effect. The resulting bounds on the amplitude of quantum fluctuations of the bubble wall from the absence of such an effect in the observed microwave background anisotropies are quite strong. We also study the contribution from a discrete long wavelength super-curvature mode ($k^2 \simeq 2m^2/3H^2$) that appears in the spectrum of open de Sitter vacuum fluctuations. We constrain the parameters of the models of open inflation so that these modes do not distort the observed temperature anisotropy.
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2 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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This is known as the “open inflation” [ref] .
Probability of Slowroll Inflation in the Multiverse · Probability for Multifield Slowroll Inflation · 0.87
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