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Based on instanton effects → exponential hierarchies → cangenerate Msusy ≪ MPl
Experimentally:
• Supersymmetry not found at LHC with M < 1TeV.
• Not excluded large field inflation: Minf ∼ MGUT
Contemplate scenario of moduli stabilization with onlypolynomial hierarchies → string tree-level with fluxes
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Introduction
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Introduction
PLANCK 2015, BICEP2 results:
• upper bound: r < 0.07
• spectral index: ns = 0.9667± 0.004 and its runningαs = −0.002± 0.013.
• amplitude of the scalar power spectrumP = (2.142± 0.049) · 10−9
Lyth bound
∆φ
Mpl∼ O(1)
√
r
0.01and
Minf = (Vinf)1
4 ∼( r
0.1
)1
4 × 1.8 · 1016GeV
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Introduction
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Introduction
Inflationary mass scales:
• Hubble constant during inflation: H ∼ 1014 GeV.
• mass scale of inflation: Vinf = M4inf = 3M2
PlH2inf ⇒
Minf ∼ 1016 GeV
• mass of inflaton during inflation: M2Θ = 3ηH2 ⇒
MΘ ∼ 1013 GeV
Large field inflation with ∆Φ > Mpl:
• Makes it important to control Planck suppressedoperators (eta-problem)
• Invoking a symmetry like the shift symmetry of axionshelps
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Axion inflation
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Axion inflation
Axions are ubiquitous in string theory so that many scenarioshave been proposed
• Natural inflation with a potentialV (θ) = Ae−SE(1− cos(θ/f)). Hard to realize in stringtheory, as f > 1 lies outside perturbative control.(Freese,Frieman,Olinto)
• Aligned inflation with two axions, feff > 1. (Kim,Nilles,Peloso)
• N-flation with many axions and feff > 1.(Dimopoulos,Kachru,McGreevy,Wacker)
Comment: These models have come under pressure by theweak gravity conjecture, which for instantons was proposed tobe f · SE < 1. (Montero,Uranga,Valenzuela),(Brown,Cottrell,Shiu,Soler)
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Axion monodromy inflation
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Axion monodromy inflation
• Monodromy inflation: Shift symmetry is broken bybranes or fluxes unwrapping the compact axion →polynomial potential for θ. (Kaloper, Sorbo), (Silverstein,Westphal)
non-pert. fluxes
Discrete shift symmetry acts also on the fluxes, i.e. one getsdifferent branches → tunneling a la Coleman-de Lucia
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Axion monodromy inflation
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Axion monodromy inflation
Recent proposal: Realize axion monodromy inflation via theF-term scalar potential induced by background fluxes.(Marchesano.Shiu,Uranga),(Hebecker, Kraus, Wittkowski),(Bhg, Plauschinn)
Advantages
• Generating the inflaton potential, supersymmetry isbroken spontaneously by the very same effect by whichusually moduli are stabilized
• Generic, as the field strengths Fp+1 = dCp +H ∧ Cp−2
involves the gauge potentials Cp−2.
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Objective
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Objective
For a controllable single field inflationary scenario, all modulineed to be stabilized such that
MPl > Ms > MKK > Minf > Mmod > Hinf > |MΘ|
Aim: Systematic study of realizing single-field fluxed F-termaxion monodromy inflation, taking into account the interplaywith moduli stabilization.
Continues the studies from (Bhg,Herschmann,Plauschinn), (Hebecker,
Mangat, Rombineve, Wittkowsky) by including the Kahler moduli.
Note:
• There exist a no-go theorem for having an unconstrainedaxion in supersymmetric minima of N = 1 supergravitymodels (Conlon)
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Introduction
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Introduction
Realistic string model building =⇒ break N=2 → N=1 viaorientifold projection
Generate a non-trivial scalar potential for the massless axionΘ by turning on additional fluxes fax and deform
Winf = λW + fax∆W .
This quite generically leads to
Mmod&pMΘ =⇒ Mmod
&pMKK
Toy model with uplifted scalar potential
V = λ2(
(hs+ f)2
16sτ3− 6hqs− 2qf
16sτ2− 5q2
48sτ
)
+θ2
16sτ3+ Vup .
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Toy model
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Toy model
Backreaction of the other moduli adiabatically adjustingduring the slow-roll of θ flattens the potential(Dong,Horn,Silverstein,Westphal)
θ
Vback
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Effective potential
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Effective potential
Large field regime: θ/λ ≫ f. The potential in the large-fieldregime becomes
Vback(Θ) =25
216
hq3λ2
f2
(
1− e−γΘ)
.
with γ2 = 28/(14 + 5λ2) (similar to Starobinsky-model).
• For θ/λ ≪ f: 60 e-foldings from the quadratic potential
• Intermediate regime: linear inflation
• For θ/λ ≫ f: Starobinsky inflation
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Tensor-to-scalar ratio
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Tensor-to-scalar ratio
λ
r
With decreasing λ the model changes from chaotic toStarobinsky-like inflation.
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Parametric control
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Parametric control
From UV-complete theory point of view, large-field inflationmodels require a hierarchy of the form
MPl > Ms > MKK > Minf > Mmod > Hinf > MΘ ,
where neighboring scales can differ by (only) a factor ofO(10).
Main observation
• the larger λ, the more difficult it becomes to separatethe high scales on the left
• for small λ, the smaller (Hubble-related) scales on theright become difficult to separate.
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Conclusions
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Conclusions
• Systematically investigated the flux induced scalarpotential for non-supersymmetric minima, where we haveparametric control over moduli and the mass scales.
• All moduli are stabilized at tree-level → the frameworkfor studying F-term axion monodromy inflation.
• Since the inflaton gets its mass from a tree-level effect,one gets a high susy breaking scale.
• As all mass scales are close to the Planck-scale, it isdifficult to control all hierarchies. Does large fieldinflation necessarily must include stringy/KK effects?
• The (MS)SM could arise on a set of intersectingD7-branes → mutual constraints between fluxes andbranes (Freed/Witten anomalies). Is sequestering,Msoft ≪ M 3