Cosmology with Extra Dimensions

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1 Cosmology with Extra Dimensions Johannes Martin University of Bonn May 13th 2005

2 Outline Motivation and Introduction 1 Motivation and Introduction Motivation From 10D to 4D: Dimensional Reduction Common Approach 2 3

3 Outline Motivation and Introduction Motivation From 10D to 4D: Dimensional Reduction Common Approach 1 Motivation and Introduction Motivation From 10D to 4D: Dimensional Reduction Common Approach 2 3

4 Motivation From 10D to 4D: Dimensional Reduction Common Approach Early Universe Late-time Universe Inflation de Sitter Geometry H Expansion rate ds 2 = dt 2 +e 2Ht d x 2 Flatness Homogeneity Monopoles Origin of structure String Dilaton/ Moduli fields LSP/ KK particles Embedding of Inflation in theory with ED Exploration of the Dark Side with EDs Cosmological Perturbations Universe: homogeneous and isotropic on large scales and early times All structure expressed as Cosmological Perturbations Powerful tool for Exploration of the Dynamics

5 Dimensional Reduction Motivation From 10D to 4D: Dimensional Reduction Common Approach General (Kaluza Klein) Procedure: Metric: «γµν A µ g MN A µ e σ R 5 R 4 ( µσ) 2 e σ F 2 µν Matter field fluctuations: φ(x, y) X n φ n(x) sin( 2πn R y) ( Mφ) 2 ( µφ) 2 + m 2 nφ 2, m n n R Important! Small extra dimensions = n = 0 states only (consistent truncation) Many additional light (moduli) fields Size, shape, topology of EDs Moduli fields = Effective couplings, charges, and masses N = 1 SUSY = Kähler and Super potential for moduli fields

6 Motivation From 10D to 4D: Dimensional Reduction Common Approach N = 1 Compactifications (Engineering) Compactifications on CY: O(100) moduli fields unstabilized, undetermined (flat directions) = disaster for phenomenology Compactifications on CY + Fluxes: Some moduli fields stabilized SUSY vacua Ω Λ < 0 Comp. on CY + Fluxes + non-perturb. Effects: All moduli stabilized Vacua with broken SUSY, Ω Λ > 0 Inflaton Potentials: Dark Energy Potentials: Dasgupta, Hsu, Kallosh, Linde, Zagermann 04 V(σ) σ Kallosh, Kachru, Linde, Trivedi 03

7 Outline Motivation and Introduction 1 Motivation and Introduction Motivation From 10D to 4D: Dimensional Reduction Common Approach 2 3

8 Braneworlds Motivation and Introduction Kaluza Klein Compactification Generic Background: ds 2 = e 2B(y) dt2 + e 2Ht d x }{{} 2 +g mn (y)dy m dy n γ µν(x)dx µ dx ν

9 Flux Compactification Action: S = d 4 xd q y { } G 1 2 R 1 2q! F2 q Λ Ansatz: ds 2 = dt 2 + e 2Ht d x 2 + ρ 2 dω 2 q F m1 m q = cε m1 m q Perturbations: Metric: Flux: Scalars δg mn a m2 m q Vectors δg µn a µm3 m q Tensors δg µν Dynamics for the Perturbations: ) δg MN = δt MN, δ (F M1 Mq ; = 0 M1

10 Universal Gravitational Instability m 2 rad = 12q 2 + q H2 + Universal appearance in models with extra dimensions q and cosmological spacetimes H Known asymptotics Can be stabilized Zero mode of the volume modulus

11 Non-perturbative Results Braneworlds S = d 5 x { } 1 g 2 R 1 2 ( φ)2 V (φ) d 4 x γ {[K] + U i (φ)} b i i=1,2 Non-linear Dynamics with the BRANECODE: J.M. et al. (2003) Brane collision Potentials V, U unimportant Anisotropic Kasner-like asymptotics Collapse of extra dimension Brane separation Transition towards stable solution with smaller H Compactifications ds p S q S = d p+q x g F m1 m q = c(t)ε m1 m q { 1 2 R Λ 1 2q! F2 q ds 2 = dt 2 + a(t) 2 d x 2 + b(t) 2 dω 2 q Phasespace Analysis: (a 0 = e Ht, b 0 ) CONTALDI, KOFMAN & PELOSO (2004) Collapse of internal space Anisotropic Kasner geometry Decompactification 11 dimensional de Sitter geometry KRISHNAN, PABAN & ZANIĆ (2005) Transitions de Sitter with smaller H Minkowski or AdS 4 }

12 Effective Potential for the Volume modulus Collaps of ED V eff (σ) 4 2 Decompactification of ED c=0 c=0.39c th c=0.42c th c=c th c=2c th σ Inflation + ED = Instabilities Limits on the scale of Inflation Interesting Dynamics? Schwindt, Wetterich 05

13 Outline Motivation and Introduction 1 Motivation and Introduction Motivation From 10D to 4D: Dimensional Reduction Common Approach 2 3

14 Idea: One of the moduli fields Dark energy Fine-tuning problem: Scales of dark energy potential Ω Λ H 0 Dynamics 1 φ + 3H 0 φ φ 2 + V V(φ) 2 (φ) = 0 w = 1 φ V(φ) ] [ δφ + 3H 0 δφ + [V (φ) + k2 δφ = 4 φ ] 2V (φ) Φ a 2 V (φ), V (φ) H 0 V (φ), V (φ) H 0 V (φ), V (φ) H 0 V(φ) V(φ) V(φ) φ w 1, w 1 0 φ w > 1, w 1 0 φ w 1, w 1 0

15 Work in Progress Numerics l(l+1)c l /(2π) [µk] Motivation and Introduction Time evolution of background+perturbations (γ,ν,cdm,b,δφ,φ) Hydrodynamical equations Collisionless Boltzmann equation = T T V run V tach V stab ΛCDM Dark energy potentials 4Λ 3Λ 2Λ Λ Dark Energy Potentials V stab (φ) V run (φ) V tach (φ) φ [M P /8π] z V run V tach V stab ΛCDM 0.2 w < 1? 0.4 a Ω (Λ) Ω (m) Anti-correlated isocurvature perturbations Hu, Gordon 04

16 Enqvist, Hannestad, Sloth 05 Ω Λ > 0 Periodic BC = effective de Sitter geometry = Event Horizon: r H = a(t) ( ) H 1 e Ht = Finite Universe! = Boundary conditions? familiar from spatially compact topologies unobserved symmetries and multiple images highly constrained Dirichlet/Neumann BC Horizon IR cutoff Dirichlet: Quantum fields vanish at cutoff scale Neumann: No current flow beyond the cutoff I I O

17 Motivation and Introduction 1 Instabilities in cosmological compactifications Limit on the scale of inflation from moduli stabilization Dynamical transitions to stable configurations possible Dynamical mechanism for lowering the CC? 2 Besides SN and WL CMB additional probe for exploration of DE CMB particular sensitive to dynamical properties of DE CMB data on largest scales vs. cosmic variance