Cosmological Moduli, Dark Matter, and Possible Implications for the - PowerPoint PPT Presentation

Cosmological Moduli, Dark Matter, and Possible Implications for the LHC Scott Watson Michigan Center for Theoretical Physics Based on work with: Berkeley: Piyush Kumar Columbia: Brian Greene, Simon Jude, Janna Levin, Amanda Weltman Davis: Nemanja Kaloper McGill: Robert Brandenberger Michigan: Sera Cremonini and Konstantin Bobkov, Gordon Kane, Jing Shao Trieste / CERN: Bobby Acharya

Standard Model Landscape R 1 Higgs Moduli Space (VEVs) 246 GeV −∞ ∞ � h � ?

Kaluza-Klein Landscape ← 2 R → � R ≡ G 55 → φ � x ) e iny/R ψ ( � x, y ) = ψ n ( � n R 1 Radion Moduli Space −∞ ∞ ? � φ �

Field Theory Moduli Spaces Observations and Puzzles • (Uncountably) Infinite number of vacua • Small masses / weak couplings? • High level of symmetry (not just a bunch of U(1)’s)? • Cosmological Constant -- Anthropics needed? 10 − 3 eV � 4 � −∞ ∞ ? Λ

Can knowledge of UV Completion address these issues? aka: String Theory

String Moduli Spaces • Couplings and masses are derived quantities g 2 s G N = M 2 s V 6 V 1 / 6 g s ∼ e � φ � ∼ e � ψ � 6 α GUT = g 2 s V 6 G N = (6 . 674280 . 00067) × 10 − 11 m 3 kg − 1 s − 2 . • Observation --> Hope for finite moduli space OR an explanation Vafa Conjecture = always finite volume

Standard Model Landscape R 1 Moduli Space (VEVs) ? −∞ ∞ � φ �

String Standard Model Landscape R 1 Moduli Space (VEVs) ? Finite Finite −∞ ∞ � φ �

String Standard Model Landscape R 1 Moduli Space (VEVs) ? Finite Finite −∞ ∞ � φ � Turn on Flux � Discretum F p = Z X

String Standard Model Landscape R 1 Moduli Space (VEVs) ? Finite Finite −∞ ∞ � φ � Turn on Flux � Discretum F p = Z X Dualities 1 � φ � ↔ � φ �

String Standard Model Landscape R 1 Moduli Space (VEVs) ? Finite Finite −∞ ∞ � φ � Turn on Flux � Discretum F p = Z X Dualities 1 � φ � ↔ � φ � Points of Enhanced Symmetry

String Theory on a Circle � R ≡ G 55 → φ ← 2 R → A R/L = G µ 5 ± B µ 5 µ

String Theory on a Circle � R ≡ G 55 → φ ← 2 R → A R/L = G µ 5 ± B µ 5 µ Additional Massive States m 2 χ = M 2 ω 2 R 2 − 4 � � s

String Theory on a Circle � R ≡ G 55 → φ ← 2 R → A R/L = G µ 5 ± B µ 5 µ Additional Massive States m 2 χ = M 2 ω 2 R 2 − 4 � � s Enhanced Symmetry R → 1 = M − 1 m χ → 0 ω = ± 2 s U (1) → SU (2)

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) Adiabaticity fails when, ˙ m χ ∼ O (1) m 2 χ � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) Adiabaticity fails when, ˙ m χ ∼ O (1) m 2 particle χ creation � ϕ � = 0 ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Motion on Moduli Space ϕ → ϕ ( t ) m χ = g φ ( t ) ( ϕ 0 , χ 0 ) Adiabaticity fails when, ˙ m χ ∼ O (1) m 2 particle χ creation � ϕ � = 0 ESP Near ESP modes become excited -Particle production- − πk 2 � � n k ≈ exp gv 0

Moduli Trapping at Enhanced Symmetry Points (ESPs) S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 Backreaction and Trapping V eff = 1 2 g 2 χ 2 ϕ ( t ) 2 � χ 2 � = ρ χ ρ χ = ω 2 g 2 ϕ 2 χ Constant Force of Attraction � ϕ � = 0 ESP ϕ ϕ = − gn χ ϕ + 3 H ˙ ¨ | ϕ |

Moduli Trapping S.W. hep-th/0404177 S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001

Moduli Trapping S.W. hep-th/0404177 S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 V ϕ

Moduli Trapping S.W. hep-th/0404177 S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 V ϕ

Moduli Trapping S.W. hep-th/0404177 S.W. hep-th/0404177, Kofman, et. al. hep-th/0403001 V 3 4 2 1 ϕ

Studies of Moduli Dynamics Toriodal Compactifications: - S.W. hep-th/0404177 Related ideas -- “String Gas Cosmology”: - T. Battefeld and S.W. -- Rev.Mod.Phys.78:435-454,2006 Conifold: - Mohaupts & Saueressig hep-th/0410272 & hep-th/0410273 - Greene, Judes, Levin, S. W., Weltman hep-th/0702220 Brane positions: - Kofman, Linde, Liu, Maloney, McAllister, Silverstein hep-th/0403001 - Silverstein-Tong hep-th/0310221 M-theory: - Cremonini & S.W. hep-th/0601082 ISS and Finite Temperature: - Craig, Fox, and Wacker hep-th/0611006 Conclusion: Moduli Trapping is generic property of moduli spaces w/ UV completion including gravity

Do we expect to encounter an ESP?

Ergodic (“Chaotic”) Motion and Vacuum Sampling Poincare Surface of Sections Motion on moduli space G ij ( ϕ ) ∂ µ ϕ i ∂ µ ϕ j χ Non-ergodic motion Ergodic Motion ϕ

Ergodic (“Chaotic”) Motion and Vacuum Sampling Poincare Surface of Sections Motion on moduli space G ij ( ϕ ) ∂ µ ϕ i ∂ µ ϕ j χ Ergodic Motion ϕ

Classical Moduli Dynamics Horne & Moore hep-th/9403058 Axio-dilaton in 4D � � ( Im τ ) 2 − κ 2 � � 1 � R − 1 ∂ µ τ∂ µ ¯ τ F − 1 d 4 x √− g aF ˜ F 2 S 4 = + . . . 4 π Tr 2 κ 2 2 g s H = SL (2 , R ) τ = a + ig − 1 s SO (2)

Classical Moduli Dynamics Horne & Moore hep-th/9403058 Axio-dilaton in 4D � � ( Im τ ) 2 − κ 2 � � 1 � R − 1 ∂ µ τ∂ µ ¯ τ F − 1 d 4 x √− g aF ˜ F 2 S 4 = + . . . 4 π Tr 2 κ 2 2 g s H = SL (2 , R ) τ = a + ig − 1 s SO (2) Additional Discrete Symmetries SL (2 , R ) 1 M = ↔ g s SO (2) × SL (2 , Z ) g s

Classical Moduli Dynamics W eak Coupling Im τ = g − 1 s Re τ = a τ → aτ + b 1 ad − bc = 1 → g s cτ + d g s

Classical Moduli Dynamics W eak Coupling Im τ = g − 1 s Re τ = a τ → aτ + b 1 ad − bc = 1 → g s cτ + d g s

Classical Moduli Dynamics W eak Coupling Im τ = g − 1 s g 2 1 s G N = = s V 6 ( Im τ ) 2 ∼ finite M 2 M 2 s V 6 Re τ = a τ → aτ + b 1 ad − bc = 1 → g s cτ + d g s

Aspects of Moduli Stabilization • Two aspects of moduli stabilization: • Generate potential -- a lot of work has been done (e.g. Fluxes, gaugino condensation, instantons etc...) • Fix at the minimum and remain there! -- ( not so much progress )

Duality fixed points are absolute extrema of effective potential for all times (protected by symmetries) e.g. see work of Dine and Banks

Moduli trapping --> why we begin there (initial conditions)

Moduli trapping --> why we begin there (initial conditions) Configurations with: more symmetry / lighter particles are favored

The “Dilaton” Sera Cremonini (Michigan) & S.W. hep-th/0601082 (see also work by Brustein) • BPS techniques suggest that attractor lies outside perturbative region • Kahler moduli typically have shift symmetry -- require non-perturbative effects

Assume “Dilaton” is stabilized at weak coupling e.g. Gaugino Condensation

Prior to Stabilization, it is a dynamical degree of freedom... It could dominate the energy density: e.g. The “Pre-Big Bang” It could be subdominant with other energy/matter present: e.g. String Gas Cosmology

Early String Universe --> FRW Universe???

Geometric Precipices in String Cosmology Nemanja Kaloper and S.W. arXiv:0712.1820 Dilaton gravity w/ sources

Geometric Precipices in String Cosmology Nemanja Kaloper and S.W. arXiv:0712.1820 Dilaton gravity w/ sources Discrete and conserved charge!!! e = NH 2 s + e φ s ρ s

Geometric Precipices in String Cosmology Nemanja Kaloper and S.W. arXiv:0712.1820 ? String Phase RDU Phase (+) (-)

Geometric Precipices in String Cosmology Nemanja Kaloper and S.W. arXiv:0712.1820 e = NH 2 s + e φ s ρ s

Geometric Precipices in String Cosmology Nemanja Kaloper and S.W. arXiv:0712.1820 e = NH 2 s + e φ s ρ s Must Violate NEC

Effect on Dark Matter / LHC