1 multi-field open inflation & instanton yitp, kyoto university kazuyuki sugimura (collaborator :...
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Multi-field Open Inflation & Instanton
YITP, Kyoto University
Kazuyuki Sugimura(Collaborator : D. Yamauchi and M. Sasaki)
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Introductions Multi-field Open Inflation
– Scenario and model– Formulation of multi-field tunneling– Multi-field instanton– Evolution after tunneling
Conclusions and Discussions
Contents
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Introductions
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Inflation and beyondhttp://lambda.gsfc.nasa.gov
Inflation solves
- Horizon problem- Flatness problem- Monopole problem
also predicts power spectrum
But
• How is it implemented in particle physics?
• How does it start?
?
very good agreement!!
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String landscape
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many physical degrees of freedom
http://journalofcosmology.com
Non-trivial structure of vacuum
- scalar field- flat potential
• In String theory- High dimensionality- Integration out of high energy physics
• implementation of inflation seems possible
(Susskind, 2003)
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String landscape
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many physical degrees of freedom
http://journalofcosmology.com
- multi-field
Non-trivial structure of vacuum
- quantum tunneling
- scalar field- flat potential
• String theory also implies
• In String theory- High dimensionality- Integration out of high energy physics
• implementation of inflation seems possible
(Susskind, 2003)
Multi-field open inflation
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Multi-field open inflation
(Multi-field) Open inflation
• Quantum tunneling before slow-roll (in multi-field system)
• Open inflation in multi-field systemmay solve a problem in single-field case
- Only an artificial potential model is known (Linde 1998)
We will study multi-field open inflation!!
- Ωk〜 -0.01 is most favorable(?) (Freivogel, et al., 2006)
possibility of curvature detectiongood point ofmulti-field system
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Multi-field open inflation
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Multi-field model witha simple potential
tunneling field σ inflaton φ
φ
σ
Contour of V(σ,φ)
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1. rolling to false vacuum2. false vacuum inflation3. quantum tunneling4. slow-roll inflation 5. reheating
rolling to false vacuum
false vacuum inflation
reheatingContour of V(σ,φ)
slow-roll inflation
quantum tunneling
Multi-field model witha simple potential
tunneling field σ inflaton φ
φ
σ
Scenario
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Formulation of multi-field tunneling with gravity
• Multi-field extension of Coleman-De Luccia instanton
- instanton
- inside of nucleated bubble is open Friedmann universe
O(4)-symmetric non-trivial Euclidean classical path
We will1. construct a multi-field instanton2. evolve the universe inside bubble
(Coleman and De Luccia, 1980)
initial state is given by instanton value at t=0
Euclidean metric
image of instantonfor single-field system
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Multi-field instanton tunneling
• inflaton φ moves during tunnelingbut a little for this parameter choice
• instanton value at t=0 gives the initial state of bubble
• multi-field instanton with gravity isexplicitly constructed for the first time
evolution after tunneling
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Evolution of inflaton φafter tunneling
reheating
slow-roll inflation
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Evolution of tunneling field σafter tunneling
slow-roll inflation
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Evolution after tunneling
reheatingslow-roll inflationcurvature dominant
energy decomposition
slow-roll inflation
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Evolution after tunneling
reheatingslow-roll inflationcurvature dominant
• tunneling field σ is massive damped
oscillation
energy decomposition
slow-roll inflation
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Evolution after tunneling
reheatingslow-roll inflationcurvature dominant
• tunneling field σ is massive damped
oscillation• curvature dillution
potential of inflatonφ gets dominant
energy decomposition
slow-roll inflation
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Evolution after tunneling
reheatingslow-roll inflationcurvature dominant
• tunneling field σ is massive damped
oscillation• curvature dillution
potential of inflatonφ gets dominant
• inflation lasts for 60 e-foldings
energy decomposition
slow-roll inflation
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Evolution after tunneling
reheatingslow-roll inflationcurvature dominant
• tunneling field σ is massive damped
oscillation• curvature dillution
potential of inflatonφ gets dominant
• inflation lasts for 60 e-foldings
energy decomposition
slow-roll inflation
first explicit open inflationmodel with simple potential!!
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Conclusions and Discussions
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Conclusions
We studied about Multi-field open inflation, which is motivated by string landscape
The Coleman De Luccia instanton method was extended to the multi-field case
Multi-field instanton with gravity and the evolution inside the bubble were explicitly calculated
Our multi-field open inflation model is the first explicit open inflation model with a simple potential
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Discussions and Future works
Method to calculate a quantum fluctuation in open inflation seems possible to be applied to our model
Interaction between heavy oscillating tunneling field and inflaton may produce some interesting features in power spectrum
Quantum tunneling changes the state of the universe from Bunch-Davies vacuum, and this may produce a characteristic non-gaussianity
If we are very lucky, we may find an evidence of our model, or string landscape, from observations
(Garriga, Montes, Sasaki, Tanaka (1998))
(now we are working!)
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Appendix
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Interaction effect on decay rate
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with multi-field dynamics
without multi-field dynamics
naive question about multi-field dynamics
Q. Do multi-field dynamics make decay rate larger, or smaller?
• decay rate
• multi-field instanton
• instanton when neglecting dynamical freedom of φ
- single field instanton for
- staying at false vacuum
(Coleman and De Luccia, 1980)
Contour of V(σ,φ)• B-B0 comes from the multi-field dynamics effect
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Multi-field dynamics effect on decay rate
A. The multi-field dynamics make decay rate larger!!
multi-field dynamics more significant
• decay rate
B
decay rate
• difference of B due to multi-field dynamics
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Decomposition of energy density in the universe after tunneling
• Hubble parameter
• inflaton φ
• tunneling field σ
• curvature
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mφ dependence of the system
different mφ
mφ changes not only the strength of interactionbut also the non-interaction part
different
• in the case of the very large mφ, theremay exist only a Hawking-Moss instanton
large mφ
small
large V0(σF)
(barrier is effectively small)