Open Inflation Instanton YITP Kyoto University Kazuyuki Sugimura Collaborator D Yamauchi and M Sasaki 2 Introductions Multifield Open I nflation Scenario and model Formulation of multifield tunneling ID: 582972
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1
Multi-field Open Inflation ＆ Instanton
YITP, Kyoto UniversityKazuyuki Sugimura(Collaborator : D. Yamauchi and M. Sasaki)Slide2
2
IntroductionsMulti-field Open InflationScenario and modelFormulation of multi-field tunnelingMulti-field instantonEvolution after tunnelingConclusions and DiscussionsContentsSlide3
Introductions
3Slide4
Inflation and beyond
4http://lambda.gsfc.nasa.govInflation solvesHorizon problemFlatness problemMonopole problem
also predicts power spectrumButHow is it implemented in particle physics?How does it start?
？
v
ery good agreement!!Slide5
String landscape
5many physical degrees of freedom http://journalofcosmology.com
Non-trivial structure of vacuum scalar fieldflat potential
In String theory
High dimensionality
Integration
out of high energy
physics
implementation of
inflation seems possible
(Susskind, 2003)Slide6
String landscape
6many physical degrees of freedom http://journalofcosmology.com
multi-fieldNon-trivial structure of vacuum quantum tunneling
s
calar 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 inflationSlide7
7
Multi-field open inflation(Multi-field) Open inflationQuantum tunneling before slow-roll (in multi-field system)Open inflation in multi-field system
may solve a problem in single-field caseOnly 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
detection
good point
of
multi-field systemSlide8
Multi-field open inflation
8Slide9
9
Multi-field model witha simple potential
tunneling field σinflaton φ
φ
σ
Contour of V(
σ,φ
)Slide10
10
rolling to false vacuumfalse vacuum inflationquantum tunnelingslow-roll inflation reheating
rolling to false vacuumfalse vacuum inflationreheating
Contour of V(
σ,φ
)
slow-roll inflation
quantum tunneling
Multi-field model with
a simple potential
tunneling field
σ
inflaton
φ
φ
σ
ScenarioSlide11
Formulation of multi-field tunneling with gravity
11Multi-field extension of Coleman-De Luccia instantoninstantoninside of nucleated bubble is open Friedmann universe
O(4)-symmetric non-trivial Euclidean classical pathWe will1. construct a multi-field instanton
2
.
evolve the universe inside bubble
(Coleman and De
Luccia
, 1980)
initial state is given by
instanton
value at t=0
Euclidean metric
image of
instanton
for single-field systemSlide12
Multi-field
instanton
tunneling
12
inflaton
φ
moves during tunneling
but a little
for this parameter choice
instanton
value at t=0 gives
the initial state of bubble
multi-field
instanton
with gravity is
explicitly constructed for the first time
evolution after tunnelingSlide13
Evolution of
inflaton φafter tunneling13reheating
slow-roll inflationSlide14
Evolution of tunneling field σ
after tunneling14slow-roll inflationSlide15
Evolution after tunneling
15reheating
slow-roll inflationcurvature dominant
energy decomposition
slow-roll inflationSlide16
Evolution after tunneling
16reheating
slow-roll inflationcurvature dominanttunneling field σ is massivedamped oscillation
energy decomposition
slow-roll inflationSlide17
Evolution after tunneling
17reheating
slow-roll inflationcurvature dominanttunneling field σ is massivedamped oscillation
curvature
dillution
potential of
inflatonφ
gets dominant
energy decomposition
slow-roll inflationSlide18
Evolution after tunneling
18reheating
slow-roll inflationcurvature dominanttunneling field σ is massivedamped oscillation
curvature
dillution
potential of
inflatonφ
gets dominant
inflation lasts for 60 e-
foldings
energy decomposition
slow-roll inflationSlide19
Evolution after tunneling
19reheating
slow-roll inflationcurvature dominanttunneling field σ is massivedamped oscillation
curvature
dillution
potential of
inflatonφ
gets dominant
inflation lasts for 60 e-
foldings
energy decomposition
slow-roll inflation
first explicit open inflation
model
with simple potential!!Slide20
Conclusions and Discussions
20Slide21
Conclusions
We studied about Multi-field open inflation, which is motivated by string landscapeThe Coleman De Luccia instanton method was extended to the multi-field caseMulti-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 potential21Slide22
Discussions and Future works
Method to calculate a quantum fluctuation in open inflation seems possible to be applied to our modelInteraction between heavy oscillating tunneling field and inflaton may produce some interesting features in power spectrumQuantum tunneling changes the state of the universe from Bunch-Davies vacuum, and this may produce a characteristic non-gaussianityIf we are very lucky, we may find an evidence of our model, or string landscape, from observations22(Garriga, Montes, Sasaki, Tanaka (1998))
(now we are working!)Slide23
Appendix
23Slide24
Interaction effect on decay rate
24Slide25
with multi-field dynamics
without multi-field dynamicsnaive question about multi-field dynamics
Q. Do multi-field dynamics make decay rate larger, or smaller? decay ratemulti-field instantoninstanton 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-B
0
comes from the multi-field dynamics effectSlide26
Multi-field dynamics effect on decay rate
26A. 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 dynamicsSlide27
Decomposition of energy density in the universe
after tunneling27Hubble parameterinflaton φtunneling field σ
curvatureSlide28
mφ
dependence of the system28
different mφmφ changes not only the strength of interactionbut also the non-interaction partdifferent
in the case of the very large
m
φ
,
there
may exist only a Hawking-Moss
instanton
large
m
φ
small
large
V
0
(
σ
F
)
(barrier is effectively small)