aligned natural inflation ippei obata ref)k. freese, j.a.frieman and a.v.olinto, phys.rev.lett. 65...
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Aligned Natural Inflation
Ippei Obata
Ref)K. Freese, J.A.Frieman and A.V.Olinto, Phys.Rev.Lett. 65 (1990) 3233-3236
Rolf Kappl, Sven Krippendorf and Hans Peter Nilles, [arXiv:1404.7127 [hep-th]]
13. June in Kobe
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Table of Contents
1. Introduction2. Natural Inflation3. Aligned Natural Inflation4. Summary
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Table of Contents
1. Introduction2. Natural Inflation3. Aligned Natural Inflation4. Summary
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Historical review
• There were some conceptual problems of the standard big bang model.
Ex)the horizon problem, the flatness problem, the monopole problem etc.
The “Inflationary universe” was proposed!
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The Inflationary Paradigm
The best idea explaining the early universe!
BICEP2 detects the evidence of inflationary era!?
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• The vacuum energy density is dominated:
• The cosmological metric is:
• Our Universe grows sufficiently:
During the Inflation…
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The Mechanism of the Inflation
• The “inflaton” plays an important role:
• The potential must be very flat:
very small!
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The interpretation on λ
• Why is so small number ?:
• We want to consider the inflation scenario which can derive such a small dynamically in particle-physics models!
• The “axionic inflation” is proposed . (Natural Inflation)
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The result of BICEP2
• The tensor-scalar ratio is:
• Quantum gravitational effects might destroy the flatness of the inflaton potential!
The axionic inflation might avoid such a problem!
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Table of Contents
1. Introduction2. Natural Inflation3. Aligned Natural Inflation4. Summary
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What is “axion”?
• A very light, weakly interacting scalar particle appearing in the framework of QCD, string theory etc.
• One of the candidates of dark matter in cosmology
• Has a flat potential as a result of shift symmetry! (in classical level)
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What is “axion”?
• We don’t want the exactly flat potential.
• The axion has additional explicit symmetry breaking.(quantum effects!)
However…
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Ex) The QCD axion
• The strong CP problem:
In the experiment,breaks the CP symmetry
the CP symmetry is strongly conserved!
We expect some mechanisms such as:
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Ex) The QCD axion
• In QCD Lagrangian, the Yukawa terms are included:
• We introduce a new symmetry in the QCD Lagrangian:
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Ex) The QCD axion
• By quantum effects, the parameter transforms:
• Then, the axion potential become:
So, we can set:
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Natural Inflation
• The potential is:
The axion slowly rolls on the potential
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( Satisfied!)
The successful BICEP2 constraints
For parameters:
We have shown the flatness of the potential naturally!
K.Freese and W.H.Kinney [arXiv:1403.5277v3 [astro-ph.CO]]
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The problem is…
• The condition is not good for the effective theory of the superstring:
• In the framework of string theory, various axion candidates might be provided.
• We explore the two axion model!(Aligned Natural Inflation)
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Table of Contents
1. Introduction2. Natural Inflation3. Aligned Natural Inflation4. Summary
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A two axion field model
• The Lagrangian density is:
• There is a flat direction if the following relation holds:
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Make the potential for inflation
• Breaking this flat direction by :
• The potential can be found:
Rolf Kappl, Sven Krippendorf and Hans Peter Nilles, [arXiv:1404.7127 [hep-th]]
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The effective Natural Inflation
• We can find the suitable basis:
Near the origin with ,
match with…
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Parametric plot of the potential
• For parameters
Rolf Kappl, Sven Krippendorf and Hans Peter Nilles, [arXiv:1404.7127 [hep-th]]
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The successful BICEP2 constraint
• The ns-r-plane profile is:
Rolf Kappl, Sven Krippendorf and Hans Peter Nilles, [arXiv:1404.7127 [hep-th]]
(On the other hand, )
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Table of Contents
1. Introduction2. Natural Inflation3. Aligned Natural Inflation4. Summary
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Summary
• We have illustrated the flatness of the inflaton potential through (Aligned) Natural Inflation scenario.
• It is worthwhile to research some related axionic models from the phenomenological point of view.
String, Extra dimension, …