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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
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 1 / 40
Outline
1 Motivation
2 Inflation
3 Eternal Inflation
4 Classical Transition
5 Simulating Colliding Bubble Universes
6 CMB Signature
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 2 / 40
FRW Universe : ds2 = −dt2 + a2dx2
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 3 / 40
Cosmic Microwave Background
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 3 / 40
Horizon Problem
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 4 / 40
Inflation
Inflation
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 5 / 40
Old Inflation
V(φ)
φ
VA
VB
I II
VA
VB
[Guth(1981)]
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 6 / 40
New Inflation
VC
IIIV(φ)
φ
d2φdt2 + 3H dφ
dt + dVdφ = 0
[Linde(1982)]
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 7 / 40
Eternal Inflation
T=0 x
T=-∞
I
II
HA-1
γA = ΓH−4A < 1 BBNdecay rate 4-Hubble volume
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 8 / 40
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
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 9 / 40
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]
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 10 / 40
Simulating Colliding Bubble Universes
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 11 / 40
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)
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 12 / 40
Square Wave Approximation
Rφamp
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Instanton Profile
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 14 / 40
Kinematics and Potential Factors
Kinematics
Lorentz factor : γ =∆x
R
Potential (φamp)
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CMB Signature
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 16 / 40
CMB Signature
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 17 / 40
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)
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 18 / 40
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
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 19 / 40
Future Work
Multi-field potential
A more motivated theory e.g. String Theory
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 20 / 40
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.
Wei Lin (Lewis), Matthew C. Johnson Cosmic Bubble Collision GRaB100, 2015 20 / 40
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