Cosmic Bubble CollisionObservable Signature of A Classical Transition

Wei Lin (Lewis)1 Matthew C. Johnson1,2

1Department of Physics and Astronomy, York UniversityToronto, On, M3J 1P3, Canada

2Perimeter Institute for Theoretical PhysicsWaterloo, Ontario N2J 2W9, Canada

GRaB100, 2015

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Outline

1 Motivation

2 Inflation

3 Eternal Inflation

4 Classical Transition

5 Simulating Colliding Bubble Universes

6 CMB Signature

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FRW Universe : ds2 = −dt2 + a2dx2

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Cosmic Microwave Background

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Horizon Problem

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Inflation

Inflation

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Old Inflation

V(φ)

φ

VA

VB

I II

VA

VB

[Guth(1981)]

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New Inflation

VC

IIIV(φ)

φ

d2φdt2 + 3H dφ

dt + dVdφ = 0

[Linde(1982)]

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Eternal Inflation

T=0 x

T=-∞

I

II

HA-1

γA = ΓH−4A < 1 BBNdecay rate 4-Hubble volume

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Classical Transition

VA

VB

VC

I II III

A A’ B’ B C

V(φ)

φ

Inationary Plateau

VA

VCVB VB

V (φ) = A1Exp

[− φ2

2∆φ12

]± A2Exp

[−(φ− σ)2

2∆φ22

]+

1

2m2(φ− φ0)2

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Previous Work

Numerically simulating colliding bubble universes in flat space weredone in [Amin et al.(2013a)Amin, Lim, and Yang,Amin et al.(2013b)Amin, Lim, and Yang,Easther et al.(2009)Easther, Giblin, Hui, and Lim]

Free Passage Approximation

In the absence of gravity −∂2t φ+ ∂2xφ = dVdφ

At the collision point ∂2t φ, ∂2xφ dV

dφ

Potential gradient is small far away from the wall dVdφ ∼ 0

δφkick = 2(φB − φA)

Bubble collision with gravity was done in [Johnson and Yang(2010),Johnson et al.(2012)Johnson, Peiris, and Lehner]

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Simulating Colliding Bubble Universes

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Towards Observable Signature

Bubble collision destroys the geometry of the universe

gij = a(τ)2(1 + 2R)γij (perturbed opened FRW)

Observables

BBM

D2 ∝ R′′(ξ0) Ωk(ξ0) ∝ a−2(ξ0)

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Square Wave Approximation

Rφamp

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Instanton Profile

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Kinematics and Potential Factors

Kinematics

Lorentz factor : γ =∆x

R

Potential (φamp)

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CMB Signature

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CMB Signature

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Trends in Kinematics and Potential Factors

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

RHF

1

2

3

4

5

6

7

8

2R

∆φ1−σβ1−σ

2 R(ξ0 =0)

0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032 0.0034 0.0036

φamp/Mp

6.5

7.0

7.5

8.0

8.5

2R

β1−∆φ1

2ξ R(ξ0 =0)

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Conclusion

Observability of a classical transition model is studied

Ωk = 0.000± 0.005 with confusion limit ±10−5

Factors affect the perturbation: Shape of the potential andKinematics

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Future Work

Multi-field potential

A more motivated theory e.g. String Theory

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References

Alan H. Guth.Inflationary universe: A possible solution to the horizon and flatnessproblems.Phys. Rev. D 23, 347, Jan 1981.

A. D. Linde.A new inflationary universe scenario: A possible solution of thehorizon, flatness, homogeneity, isotropy and primordial monopoleproblems.Physics Letters B, 108 (6):389 – 393, 1982.

Mustafa A. Amin, Eugene A. Lim, and I-Sheng Yang.A Clash of Kinks: Phase shifts in colliding non-integrable solitons.2013a.

Mustafa A. Amin, Eugene A. Lim, and I-Sheng Yang.A scattering theory of ultra-relativistic solitons.2013b.

Richard Easther, Jr Giblin, John T., Lam Hui, and Eugene A. Lim.Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 20 / 40

A New Mechanism for Bubble Nucleation: Classical Transitions.Phys.Rev., D80:123519, 2009.doi: 10.1103/PhysRevD.80.123519.

Matthew C. Johnson and I-Sheng Yang.Escaping the crunch: Gravitational effects in classical transitions.Phys.Rev., D82:065023, 2010.doi: 10.1103/PhysRevD.82.065023.

Matthew C. Johnson, Hiranya V. Peiris, and Luis Lehner.Determining the outcome of cosmic bubble collisions in full GeneralRelativity.Phys.Rev., D85:083516, 2012.doi: 10.1103/PhysRevD.85.083516.

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