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Higgs Inflationand
the Refined dS Conjecture
Lee Sung Mook (Yonsei U.)イ・ソンムク
arXiv:1811.03622Phys.Lett.B789 (2019) 336-340
In collaboration withCheong Dhong Yeon (Yonsei U.), Park Seong Chan (Yonsei U.)
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Contents
Higgs Inflation
De Sitter Conjecture
Analysis & Results
Summary
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Higgs Inflation
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Inflationary Cosmology – Why Inflation?
• “A theory of exponential expansion of space in the early universe”
• Horizon & Flatness Problem
• Initial Fluctuations → Large Scale Structure
• Each Inflation model has an expected values of spectral index(𝑛𝑛𝑠𝑠)
and scalar to tensor ration(𝑟𝑟).
- Wikipedia
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Inflationary Cosmology – Why Inflation?
• Slow roll parameters
• Relations between &
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Higgs Inflation
• “The Standard Model Higgs boson as the inflaton”[Fedor Bezrukov, Mikhail Shaposhnikov (2008)]
• Non-minimal coupling to Ricci scalar is assumed.
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arXiv:0710.3755
Higgs InflationUnitary gauge
RemovingNon-minimal Coupling
Weyl Transformation
Field Redefinition
Canonical kinetic term
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Higgs Inflation
Inflationary predictions :
[Fedor Bezrukov, Mikhail Shaposhnikov, 2008]
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De Sitter Conjecture
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Swampland Conjecture• For a quantum gravity theory (string theory) to be consistent with low energy effective theory (standard model), so-called Swampland Conjecture has to be satisfied.
[Gary Shiu, “QG and the Swampland”]
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[C. Vafa (2005)]
“consistent-looking semiclassical effective field theories,
which are actually inconsistent.”
arXiv:hep-th/0509212
de Sitter(dS) Derivative Conjecture
• (Refined) de Sitter derivative conjecture
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OR[H. Ooguri, E. Palti, G. Shiu, and C. Vafa (2018)]
[G. Obied, H. Ooguri, L. Spodyneiko, and C. Vafa (2018)]
Black hole entropy argumentDistance conjecture
De Sitter spaceIn quantum gravity
arXiv:1806.08362
arXiv:1810.05506
Analysis & Results
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REMINDER
Bound from the Observation
Equivalently,
De Sitter conjecture ⇔ Slow roll parameters
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Bound from the Observation
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Bound from the Observation
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Bound from the Observation
“SWAMPLAND”
“LANDSCAPE”
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[DY Cheong, SML, SC Park (2019)]
Bound from the Higgs inflation
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For 60(50) e-folds,
Condition1.
Condition2.
Bound from the Higgs inflation
[Case1]
[Case2]
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Results & Implications[DY Cheong, SML, SC Park (2019)]
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𝑐𝑐1 & 𝑐𝑐2~𝑂𝑂 1 is not satisfied simultaneously just from the observation
Requirement of 𝑐𝑐2~𝑂𝑂 1 is not strict→ Still possible to be in the landscape
In HI case, absolute bound for 𝑐𝑐1 is ~1.6
Adding Condition2 is crucial for HI to be in the landscape
Summary
Recently proposed dS conjecture provides the direct criterion for the consistency between QG and the low energy effective theories.
Slow-roll single field Inflation models can be in the landscape region, although it is in the disfavored region. ( 𝑐𝑐2~𝑂𝑂 0.01 )
→ More precise statement/argument is demanded.
Other inflationary models (e.g. quintessence, multi-field inflation) arealso needed to be considered.
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THANK YOU!ありがとうございます
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