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

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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:

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SLIDE 1

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

Cosmological Moduli, Dark Matter, and Possible Implications for the LHC

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SLIDE 2

R1 h

246 GeV

∞ −∞

Standard Model Landscape

Higgs Moduli Space (VEVs)

?

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SLIDE 3

R ≡

  • G55 → φ

← 2R →

ψ( x, y) =

  • n

ψn( x) einy/R

Kaluza-Klein Landscape

∞ −∞ φ R1

Radion Moduli Space

?

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SLIDE 4

Field Theory Moduli Spaces

  • (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?

Observations and Puzzles

  • 10−3 eV

4

Λ

∞ −∞ ?

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SLIDE 5

Can knowledge of UV Completion address these issues?

aka: String Theory

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SLIDE 6

GN = g2

s

M 2

s V6

V 1/6

6

∼ eψ

gs ∼ eφ

GN = (6.674280.00067) × 10−11 m3 kg−1 s−2.

αGUT = g2

s

V6

String Moduli Spaces

  • Couplings and masses are derived quantities
  • Observation -->

Hope for finite moduli space OR an explanation Vafa Conjecture = always finite volume

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SLIDE 7

R1 ∞ −∞

Standard Model Landscape

Moduli Space (VEVs)

φ ?

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SLIDE 8

R1 ∞ −∞

Standard Model Landscape

Moduli Space (VEVs)

φ

String

Finite Finite

?

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SLIDE 9

R1 ∞ −∞

Standard Model Landscape

Moduli Space (VEVs)

φ

String

Finite Finite

  • X

Fp = Z

Turn on Flux

Discretum

?

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SLIDE 10

R1 ∞ −∞

Standard Model Landscape

Moduli Space (VEVs)

φ

String

Finite Finite

  • X

Fp = Z

Turn on Flux

Discretum

φ ↔ 1 φ

Dualities

?

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SLIDE 11

R1 ∞ −∞

Standard Model Landscape

Moduli Space (VEVs)

φ

String

Finite Finite

  • X

Fp = Z

Turn on Flux

Discretum

φ ↔ 1 φ

Dualities

?

Points of Enhanced Symmetry

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SLIDE 12

R ≡

  • G55 → φ

← 2R →

AR/L

µ

= Gµ5 ± Bµ5

String Theory on a Circle

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SLIDE 13

R ≡

  • G55 → φ

← 2R →

AR/L

µ

= Gµ5 ± Bµ5

String Theory on a Circle

Additional Massive States

m2

χ = M 2 s

  • ω2R2 − 4
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SLIDE 14

R ≡

  • G55 → φ

← 2R →

AR/L

µ

= Gµ5 ± Bµ5

String Theory on a Circle

mχ → 0

U(1) → SU(2)

ω = ±2

R → 1 = M −1

s

Enhanced Symmetry Additional Massive States

m2

χ = M 2 s

  • ω2R2 − 4
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SLIDE 15

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

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

ϕ = 0

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SLIDE 16

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

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

ϕ = 0

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SLIDE 17

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

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

ϕ = 0

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SLIDE 18

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

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

ϕ = 0

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SLIDE 19

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

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

ϕ = 0

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SLIDE 20

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

˙ mχ m2

χ

∼ O(1)

Adiabaticity fails when,

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

ϕ = 0

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SLIDE 21

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

˙ mχ m2

χ

∼ O(1)

Adiabaticity fails when,

particle creation

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

ϕ = 0

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SLIDE 22

ESP

(ϕ0, χ0)

Moduli Trapping at Enhanced Symmetry Points (ESPs)

ϕ → ϕ(t)

mχ = gφ(t)

Motion on Moduli Space

˙ mχ m2

χ

∼ O(1)

Adiabaticity fails when,

particle creation

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

ϕ = 0

nk ≈ exp

  • −πk2

gv0

  • Near ESP modes become excited
  • Particle production-
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SLIDE 23

ESP

Moduli Trapping at Enhanced Symmetry Points (ESPs)

Veff = 1 2g2χ2ϕ(t)2

Backreaction and Trapping

χ2 = ρχ ω2

χ

= ρχ g2ϕ2

¨ ϕ + 3H ˙ ϕ = −gnχ ϕ |ϕ|

Constant Force of Attraction

ϕ = 0

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

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SLIDE 24

Moduli Trapping

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

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SLIDE 25

Moduli Trapping

V

S.W. hep-th/0404177

ϕ

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

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SLIDE 26

Moduli Trapping

V

S.W. hep-th/0404177

ϕ

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

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SLIDE 27

Moduli Trapping

V 3 2 1 4

S.W. hep-th/0404177

ϕ

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

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SLIDE 28

Studies of Moduli Dynamics

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

Toriodal Compactifications:

  • S.W. hep-th/0404177

Related ideas -- “String Gas Cosmology”:

  • T. Battefeld and S.W. -- Rev.Mod.Phys.78:435-454,2006

Conclusion: Moduli Trapping is generic property of moduli spaces w/ UV completion including gravity

M-theory:

  • Cremonini & S.W. hep-th/0601082

ISS and Finite Temperature:

  • Craig, Fox, and Wacker hep-th/0611006
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SLIDE 29

Do we expect to encounter an ESP?

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SLIDE 30

ϕ

Ergodic (“Chaotic”) Motion and Vacuum Sampling

Poincare Surface of Sections Ergodic Motion

Gij(ϕ)∂µϕi∂µϕj

Motion on moduli space Non-ergodic motion

χ

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SLIDE 31

ϕ

Ergodic (“Chaotic”) Motion and Vacuum Sampling

Poincare Surface of Sections Ergodic Motion

Gij(ϕ)∂µϕi∂µϕj

Motion on moduli space

χ

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SLIDE 32

H = SL(2, R) SO(2)

S4 = 1 2κ2

  • d4x√−g
  • R − 1

2 ∂µτ∂µ¯ τ (Imτ)2 − κ2 4π Tr

  • aF ˜

F − 1 gs F 2

  • + . . .
  • τ = a + ig−1

s

Classical Moduli Dynamics

Horne & Moore hep-th/9403058

Axio-dilaton in 4D

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SLIDE 33

H = SL(2, R) SO(2)

S4 = 1 2κ2

  • d4x√−g
  • R − 1

2 ∂µτ∂µ¯ τ (Imτ)2 − κ2 4π Tr

  • aF ˜

F − 1 gs F 2

  • + . . .
  • τ = a + ig−1

s

Classical Moduli Dynamics

Horne & Moore hep-th/9403058

Axio-dilaton in 4D

M = SL(2, R) SO(2) × SL(2, Z)

1 gs ↔ gs

Additional Discrete Symmetries

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SLIDE 34

Classical Moduli Dynamics

Im τ = g−1

s

Re τ = a τ → aτ + b cτ + d

ad − bc = 1

1 gs → gs

Weak Coupling

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SLIDE 35

Classical Moduli Dynamics

Im τ = g−1

s

Re τ = a τ → aτ + b cτ + d

ad − bc = 1

1 gs → gs

Weak Coupling

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SLIDE 36

Classical Moduli Dynamics

Im τ = g−1

s

Re τ = a τ → aτ + b cτ + d

ad − bc = 1

1 gs → gs

Weak Coupling

GN = g2

s

M 2

s V6

= 1 M 2

s V6(Im τ)2 ∼ finite

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SLIDE 37

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 )
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SLIDE 38

Duality fixed points are absolute extrema of effective potential for all times (protected by symmetries)

e.g. see work of Dine and Banks

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SLIDE 39
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SLIDE 40

Moduli trapping

  • -> why we begin there (initial conditions)
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SLIDE 41

Moduli trapping

  • -> why we begin there (initial conditions)

Configurations with: more symmetry / lighter particles are favored

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SLIDE 42

The “Dilaton”

  • BPS techniques suggest that attractor lies outside perturbative region
  • Kahler moduli typically have shift symmetry -- require non-perturbative effects

Sera Cremonini (Michigan) & S.W. hep-th/0601082 (see also work by Brustein)

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SLIDE 43

Assume “Dilaton” is stabilized at weak coupling

e.g. Gaugino Condensation

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SLIDE 44

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

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SLIDE 45

Early String Universe --> FRW Universe???

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SLIDE 46

Geometric Precipices in String Cosmology

Nemanja Kaloper and S.W. arXiv:0712.1820

Dilaton gravity w/ sources

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SLIDE 47

Geometric Precipices in String Cosmology

Nemanja Kaloper and S.W. arXiv:0712.1820

Dilaton gravity w/ sources

Discrete and conserved charge!!! e = NH2

s + eφsρs

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SLIDE 48

Geometric Precipices in String Cosmology

Nemanja Kaloper and S.W. arXiv:0712.1820

String Phase RDU Phase

?

(+) (-)

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SLIDE 49

Geometric Precipices in String Cosmology

Nemanja Kaloper and S.W. arXiv:0712.1820

e = NH2

s + eφsρs

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SLIDE 50

Geometric Precipices in String Cosmology

Nemanja Kaloper and S.W. arXiv:0712.1820

e = NH2

s + eφsρs

Must Violate NEC

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SLIDE 51

Effect on Dark Matter / LHC

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SLIDE 52

p = 0

Approximate Moduli

∆Φ → ∆E

Scalar Condensate forms

ρm ∼ 1 a3

Typically evolve like pressure-less matter

Density grows relative to radiation

  • -> Danger for BBN!

V (ϕ)

ϕ

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SLIDE 53

ΩX = Ωstd

X

ρ ρr

Scalars and CDM Inverse Problem

ΩX ∼ mX σvTr ∼ Ωstd

X

Tf Tr

  • Modified expansion

Non-thermal Production

  • Modified Expansion History -- larger cross-sections allowed
  • Non-thermal Production -- larger cross-sections allowed
  • Entropy Production can dilute existing CDM
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SLIDE 54

ΩX = Ωstd

X

ρ ρr

Scalars and CDM Inverse Problem

ΩX ∼ mX σvTr ∼ Ωstd

X

Tf Tr

  • Modified expansion

Non-thermal Production

All have parametric dependence on fundamental theory !!!!

  • Modified Expansion History -- larger cross-sections allowed
  • Non-thermal Production -- larger cross-sections allowed
  • Entropy Production can dilute existing CDM
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SLIDE 55

Ωlsph2 = 0.27

  • mlsp

100 GeV 3 3.26 × 10−7GeV −2 σv 4 DX 1/2 2 m3/2 mXi 3/2 100 TeV m3/2 3/2

G2 Result

Arxiv:0804.0863 B. Acharya, K. Bobkov, G. Kane, P . Kumar, J. Shao and S.W.

Best case for relic density Sensitive to moduli stabilization and underlying geometry

Ωcdm h2 = 0.111 ± 0.006

WMAP

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SLIDE 56

Given larger cross-sections: Can we detect decays in the galactic halo today?

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SLIDE 57

Wino-like Neutralinos - Positron Excess

χ + χ → W + W → e+ + X

Wino leading decay channel: Could excess be due to annihilating dark matter?

Flux ∼ σv ×

  • ρhalo

χ

mχ 2

Bino-like requires large “boost” factor

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SLIDE 58

Positron Excess -- Annihilating Dark Matter?

Energy (GeV )

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SLIDE 59

Positron Excess -- Annihilating Dark Matter?

Energy (GeV )

Pamela data on the way...?

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SLIDE 60

Summary

  • Early universe / high energy -- landscape is sampled in finite time
  • Vacua with higher symmetry are attractors
  • Dynamics suggest slightly broken symmetries and light masses are possible

( stabilize near ESPs)

  • Many vacua ruled out by their origin (branch) and *dis*connection with our late

time universe (Precipices of the Landscape)

  • Not enough to find a vacuum,

we must now how we cosmologically evolved here

  • Not too early to think about experiment -- hints -- inflation / dark matter?
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SLIDE 61

String Landscape?

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SLIDE 62