Minimalistic axion monodromy with an ultra-light throat mode Jakob Moritz DESY July 04, 2017 Theoretical Approaches to Cosmic Acceleration, Leiden A. Hebecker, JM, A. Westphal, L.T. Witkowski [arXiv:1512.04463] + ongoing work with Sascha Leonhardt Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 1 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Interesting because: Observable tensor modes in CMB require ∆ φ & M p . [ Lyth ’96 ] 1 Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Interesting because: Observable tensor modes in CMB require ∆ φ & M p . [ Lyth ’96 ] 1 As a matter of principle: General lessons about Quantum Gravity? 2 Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Interesting because: Observable tensor modes in CMB require ∆ φ & M p . [ Lyth ’96 ] 1 As a matter of principle: General lessons about Quantum Gravity? 2 To fit the CMB power spectrum, overall scale of the potential has to be kept small over large range of inflaton. Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Interesting because: Observable tensor modes in CMB require ∆ φ & M p . [ Lyth ’96 ] 1 As a matter of principle: General lessons about Quantum Gravity? 2 To fit the CMB power spectrum, overall scale of the potential has to be kept small over large range of inflaton. Ideal inflaton candidates: Axions, due to their perturbative continuous shift symmetry φ � ! φ + const . Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Interesting because: Observable tensor modes in CMB require ∆ φ & M p . [ Lyth ’96 ] 1 As a matter of principle: General lessons about Quantum Gravity? 2 To fit the CMB power spectrum, overall scale of the potential has to be kept small over large range of inflaton. Ideal inflaton candidates: Axions, due to their perturbative continuous shift symmetry φ � ! φ + const . Non-perturbative instanton corrections yield periodic potential V ( φ ) = Λ 4 (1 � cos( φ / f )) + ... (1) Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Large field inflation and axions Open question: Is it possible to construct models of large field inflation in string theory? Interesting because: Observable tensor modes in CMB require ∆ φ & M p . [ Lyth ’96 ] 1 As a matter of principle: General lessons about Quantum Gravity? 2 To fit the CMB power spectrum, overall scale of the potential has to be kept small over large range of inflaton. Ideal inflaton candidates: Axions, due to their perturbative continuous shift symmetry φ � ! φ + const . Non-perturbative instanton corrections yield periodic potential V ( φ ) = Λ 4 (1 � cos( φ / f )) + ... (1) ! continuous shift symmetry broken to φ � ! φ + 2 π f . Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 2 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. This is hard to realize in controlled string compactifications. Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. This is hard to realize in controlled string compactifications. Possible ways out: axion-alignment [ Kim,Nilles,Peloso’05/... ], N -flation [ Dimopoulos,Kachru,McGreevy,Wacker’05 ] Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. This is hard to realize in controlled string compactifications. Possible ways out: axion-alignment [ Kim,Nilles,Peloso’05/... ], N -flation [ Dimopoulos,Kachru,McGreevy,Wacker’05 ] But: These have come under pressure by arguments based on the ’weak gravity conjecture’ [ Arkani-Hamed,Motl,Nicolis,Vafa’06 ] [ Rudelius’15/Montero,Uranga,Valenzuela’15/Brown,Cottrell,Shiu,Soler’15... ] Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. This is hard to realize in controlled string compactifications. Possible ways out: axion-alignment [ Kim,Nilles,Peloso’05/... ], N -flation [ Dimopoulos,Kachru,McGreevy,Wacker’05 ] But: These have come under pressure by arguments based on the ’weak gravity conjecture’ [ Arkani-Hamed,Motl,Nicolis,Vafa’06 ] [ Rudelius’15/Montero,Uranga,Valenzuela’15/Brown,Cottrell,Shiu,Soler’15... ] Less constrained alternative: ’axion monodromy’ [ Silverstein,Westphal ’08 ] Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. This is hard to realize in controlled string compactifications. Possible ways out: axion-alignment [ Kim,Nilles,Peloso’05/... ], N -flation [ Dimopoulos,Kachru,McGreevy,Wacker’05 ] But: These have come under pressure by arguments based on the ’weak gravity conjecture’ [ Arkani-Hamed,Motl,Nicolis,Vafa’06 ] [ Rudelius’15/Montero,Uranga,Valenzuela’15/Brown,Cottrell,Shiu,Soler’15... ] Less constrained alternative: ’axion monodromy’ [ Silverstein,Westphal ’08 ] ! Break the periodicity of the axion weakly by introducing � ’monodromic’ potential: Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Axion monodromy Problem: Such a potential requires super-Planckian decay constants f � M p to produce at least 60 e-folds of inflation. This is hard to realize in controlled string compactifications. Possible ways out: axion-alignment [ Kim,Nilles,Peloso’05/... ], N -flation [ Dimopoulos,Kachru,McGreevy,Wacker’05 ] But: These have come under pressure by arguments based on the ’weak gravity conjecture’ [ Arkani-Hamed,Motl,Nicolis,Vafa’06 ] [ Rudelius’15/Montero,Uranga,Valenzuela’15/Brown,Cottrell,Shiu,Soler’15... ] Less constrained alternative: ’axion monodromy’ [ Silverstein,Westphal ’08 ] ! Break the periodicity of the axion weakly by introducing � ’monodromic’ potential: ! φ + 2 π f ! V + ∆ V (2) φ � ) V � Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 3 / 16
Introduction Realizations in string theory and their problems I: type IIB string theory contains RR 2-form C 2 , with gauge symmetry C 2 � ! C 2 + d Λ 1 (3) Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 4 / 16
Introduction Realizations in string theory and their problems I: type IIB string theory contains RR 2-form C 2 , with gauge symmetry C 2 � ! C 2 + d Λ 1 (3) Goal: Generate (non-periodic) potential for axions in 4 d : 1 Z a i = [ Σ i C 2 , 2 ] 2 H 2 ( M ) (4) 2 πα 0 Σ i 2 Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 4 / 16
Introduction Realizations in string theory and their problems I: type IIB string theory contains RR 2-form C 2 , with gauge symmetry C 2 � ! C 2 + d Λ 1 (3) Goal: Generate (non-periodic) potential for axions in 4 d : 1 Z a i = [ Σ i C 2 , 2 ] 2 H 2 ( M ) (4) 2 πα 0 Σ i 2 Early idea: Wrap an NS 5 brane around some 2-cycle [ McAllister,Silverstein,Westphal ’08 ] Jakob Moritz (DESY) Minimalistic axion monodromy with an ultra-light throat mode July 04, 2017 4 / 16
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