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POST-INFLATIONARY HIGGS RELAXATION AND THE ORIGIN OF MATTER-ANTIMATTER ASYMMETRY
LOUIS YANG (楊智軒) UNIVERSITY OF CALIFORNIA, LOS ANGELES (UCLA) DEC 27, 2016 NATIONAL TSING HUA UNIVERSITY
OUTLINE • Big Bang Cosmology • Inflation
• Cosmological Horizon • Brief History of the Early Universe • Quantum Fluctuations
• The Higgs Potential • Metastable of Our Vacuum • Higgs Relaxation
• Matter-Antimatter Asymmetry
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BIG BANG COSMOLOGY
3
Big Bang Dark Energy
Domination Radiation Domination (Photons)
?
𝜌 ∝ const. 𝑝 = −𝜌
𝜌 ∝ 𝑎−3 𝑝 = 0 𝑎 ∝ 𝑡2/3 𝐻 = 2/3𝑡
𝜌 ∝ 𝑇4 ∝ 𝑎−4
𝑝 =13𝜌
𝑎 ∝ 𝑡1/2 𝐻 = 1/2𝑡 time
size
𝑧~3400
𝑧~0.3
Matter Domination (Dark Matter)
CMB 𝑧 ≈ 1100
Reionization 𝑧 ≈ 10 now
𝑑𝑠2 = 𝑑𝑡2 − 𝑎2(𝑡)𝑑𝑥2
THE HORIZON PROBLEM
Our universe is very homogeneous and isotropic. 𝛿𝛿𝛿
~10−5
4 CMB Temperature map from Planck
300,000 years
300,000 years
SHORTCOMINGS OF THE BIG BANG COSMOLOGY
1. Large-scale Smoothness 𝜹𝜹𝜹
~𝟏𝟎−𝟓
2. Very flat 𝛀𝐊 < 𝟎.𝟎𝟎𝟓
3. Scale invariant spectrum for Small-scale structure.
4. Unwanted relics: GUT predict Magnetic monopoles. Why don’t see any?
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INFLATION • A period in the early universe that
the space expands very fast 𝒂 𝒕 ∝ 𝒆𝒕 𝑯𝑰
𝑯𝑰: Hubble parameter • �̇� 𝒂⁄ = 𝑯𝑰 is constant. • Everything is diluted extremely
fast! • A Horizon appears at a fixed
distance. 6
time
size
Inflation
Reheating
Radiation Domination
Matter Domination
COSMOLOGICAL HORIZON Distance to the Horizon:
𝒍𝑯 ~ 𝑯−𝟏 Beyond the horizon, star light haven’t reach us yet. Matter or Radiation domination:
• Hubble rate decreases 𝐻 ∝ 1/𝑡
• Horizon size increases with time • Stars go inside the horizon.
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𝐻−1
Horizon
COSMOLOGICAL HORIZON Inflation:
• Hubble rate 𝐻𝐼 fixed • Horizon size fixed • Particle moved outside the
horizon
• Like surrounding by a backhole horizon
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𝐻𝐼−1
Horizon
INFLATION A small patches of the universe which is in causal contact can expand to the size of current observable universe.
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Horizon
Patch of Universe in thermal
equilibrium
Horizon Inflation
Observable universe
After Inflation
Patch of Universe expands Homogeneous
Universe
𝑁 ≃ 60
× 𝑒60 Rad. and
Matter periods
EVOLUTION OF INFLATON 𝑰 Need vacuum energy domination period: Inflaton 𝑰 𝒕
�̈� + 𝟑𝑯�̇� +𝒅𝒅 𝑰𝒅𝑰
= 𝟎
1. Slow Rolling of 𝐼 • 𝐼̈ ≪ 𝑑𝑑/𝑑𝐼 and 𝐼2̇ ≪ 𝑑 • 3𝐻𝐼 ̇dominates • 𝝆 ≈ V𝑰 constant
2. Coherent oscillations
• 𝑑~ 12𝑚𝐼2𝐼2
• Matter-like
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Slow-Roll
V(I)
ΛI
I
Coherent Oscillations
BRIEF HISTORY OF EARLY UNIVERSE 1. Inflation:
• Slow-rolling regime • 𝑎 𝑡 ∝ exp (𝑡 𝐻𝐼) • Temperature 𝑇 → 0
2. Reheating: • Coherent oscillations • Matter domination • 𝐻 ≈ 2/3𝑡 • Inflaton decays • Temperature increases
3. Radiation domination
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time
size
Inflation
Reheating
Radiation
Dom
ination
Matter
Dom
ination
QUANTUM FLUCTUATION QM: Vacuum is not empty! Quantum fluctuation even for ground state.
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P(ϕ) V(ϕ)
𝜙
They are only virtual particles in flat space. But becomes real during Inflation.
QUANTUM FLUCTUATION DURING INFLATION
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Horizon Horizon
• During inflation, quantum fluctuations get amplified. • They becomes classical when the wavelength exits the
horizon. • 𝝓(𝒕) is doing like Brownian motion
Inflation 𝜙(𝑥)
Becomes classical Quantum fluctuation
𝜙0 ≠ 0
QUANTUM FLUCTUATION DURING INFLATION • Quantum fluctuation can bring the field to non-zero value. • But classical rolling down requires very long time (slow-
rolling). (Remember the 3𝐻𝐼 ̇term) • A non-zero VEV of the scalar field is building up.
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V(ϕ)
ϕ ϕmin
Quantum Jump
Can’t Roll Down Classically
Bunch, Davies (1978); Linde (1982); Hawking, Moss (1982); Starobinsky (1982); Vilenkin, Ford (1982); Starobinsky, Yokoyama (1994).
QUANTUM FLUCTUATION AS THE SEED • Fluctuation in the inflation field:
𝜹𝑰 ≃ 𝑯𝑰
𝟐𝟐
independent of wavelength 𝒌. • Scale invariant spectrum • Field fluctuation turns into Density
fluctuations: 𝜹𝝆𝝆≈𝒅′
𝒅𝜹𝑰
during reheating. • Becomes seeds of structure formation
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QUANTUM FLUCTUATION FOR OTHER FIELDS • Massless field:
𝝓𝟎 = 𝝓𝟐 ≈𝑯𝑰
𝟐𝟐𝑵
𝑁: number of e-fold of inflation
• Massive case 𝒅 𝝓 = 𝟏𝟐𝒎𝟐𝝓𝟐:
𝝓𝟎 ≃𝟑𝟖𝟐𝟐
𝑯𝑰𝟐
𝒎
• For 𝐕(𝝓) = 𝝀𝟒𝝓𝟒:
𝝓𝟎 ≃ 𝟎.𝟑𝟑𝑯𝑰/𝝀𝟏/𝟒 • In general:
𝒅 𝝓𝟎 ~ 𝑯𝑰𝟒
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V(ϕ)
ϕ ϕmin
Quantum Jump
Roll Down Classically
THE HIGGS BOSON • In 2012, LHC has found the Higgs
boson. 𝒅 𝚽 = −𝒎𝟐𝚽+𝚽 + 𝝀 𝚽+𝚽 , where 𝚽 = 𝟏
𝟐𝟎
𝒗 + 𝒉 .
• Higgs boson mass: 𝑴𝒉 = 𝟏𝟐𝟓.𝟎𝟎 ± 𝟎.𝟐𝟏 ± 𝟎.𝟏𝟏 GeV.
• A small 𝝀 𝝁� = 𝑴𝒕 ≈ 𝑴𝒉𝟐 𝟐𝒗𝟐⁄ ≈ 𝟎.𝟏𝟐𝟎
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𝒅(𝝓)
𝝓 Electroweak Vacuum
h
𝑣
C. Patrignani et al.(Particle Data Group), Chin. Phys. C, 40, 100001 (2016).
• QFT: Coupling constants changes with energy scale 𝝁
• Needs RGE • If no new physics, 𝝀 𝒉
becomes very small and turns negative at 𝝁 ≳ 𝟏𝟎𝟏𝟎 − 𝟏𝟎𝟏𝟐 GeV.
RUNNING OF 𝜆
Figure from D. Buttazzo et al., arXiv:1307.3536 [hep-ph]
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J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph]
THE HIGGS EFFECTIVE POTENTIAL • Another minimum in the potential: Planckain vacuum!!
• Much lower than the electroweak vacuum. • QM: Our universe can tunnel to the Planckain vacuum • Our universe might end in a big crunch!
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𝒔𝒔𝒔𝒔 𝒅 𝒍𝒍𝒔 𝒅 𝝓
𝒍𝒍𝒔 𝝓
Our Electroweak Vacuum
Planckian Vacuum
~1010 − 1012 GeV
h
h
METASTABLE OF OUR VACUUM Our universe is right on the meta-stable region.
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J. Elias-Miro et al., Phys. Lett. B709, 222 (2012) G. Degrassi et al., JHEP 1208, 098 (2012) D. Buttazzo et al., arXiv:1307.3536 [hep-ph]
LARGE HIGGS VEV DURING INFLATION • Higgs has a shallow potential at large scale. • Large Higgs vacuum expectation value (VEV) during
inflation.
• For 𝐕(𝝓) = 𝝀𝟒𝝓𝟒:
𝝓𝟎 ≃ 𝟎.𝟑𝟑𝑯𝑰/𝝀𝟏/𝟒 • For inflationary scale 𝚲𝐈 = 𝟏𝟎𝟏𝟑 GeV, the Hubble rate
𝑯𝑰 = 𝚲𝐈𝟐
𝟑𝑴𝒑𝒍~𝟏𝟎𝟏𝟑 GeV, and 𝝀~𝟎.𝟎𝟏, the Higgs VEV after
inflation is 𝝓𝟎 ~ 𝟏𝟎𝟏𝟑GeV.
• For such a large VEV, the scalar field can be sensitive to higher dimensional operators.
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POST-INFLATIONARY HIGGS RELAXATION • During reheating, the Higgs field relaxes and oscillates. • Amplitude decreases due to the Hubble friction.
�̈� + 𝟑𝑯�̇� +𝒅𝒅 𝝓,𝜹𝒅𝝓
= 𝟎
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• Relaxation time 𝑡𝑟𝑟𝑟 ~ 𝑇𝑅𝑅
4 3⁄ 𝑡𝑅𝑅−1/3 or
𝑡𝑟𝑟𝑟~ 7 𝜆1 4⁄ 𝜙0⁄ • Happens during
reheating • Breaks time reversal
symmetry, and is out of thermal equilibrium.
• An important epoch!
MATTER-ANTIMATTER ASYMMETRY • In 1928, Paul Dirac wrote down the Dirac equation, and
predict the existence of anti-particle. • Fundamental theory of particle physics seems symmetric
between particle and anti-particle. • We only see matter (baryons) in our universe. • CMB observations:
𝜼𝑩 =𝒔𝑩 − 𝒔𝑩�
𝒔𝜸≅ 𝟑 × 𝟏𝟎−𝟏𝟎
• Baryogenesis: Doesn’t work quite well. • Leptogenesis:
Make the lepton asymmetry first. Then later turns them into baryon asymmetry by Sphaleron process.
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SAKHAROV CONDITIONS Successfully Baryo- / Lepto-genesis requires: 1. Deviation from thermal equilibrium Post-inflationary Higgs relaxation
2. 𝑪 (Charge) and 𝑪𝑪 (Charge & Parity) violations 𝑪𝑪 phase in the quark sector, higher dimension
operator, … 3. Baryon or Lepton number violation Right-handed Majorana neutrino
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Andrei D. Sakharov (1967)
𝒪6 OPERATOR • During the relaxation, the scalar field can be sensitive to
higher dimensional operators.
• Consider the derivative couplings like
𝒪6 = − 1Λ𝑛2
𝜕𝜇 𝜙 2 𝑗𝐵+𝐿𝜇 or 𝒪5 = − 1
Λ𝑛𝜕𝜇𝜙 𝑗𝐵+𝐿
𝜇
• Effective chemical potentials for baryon and lepton number
𝜇eff, 6 = − 1Λ𝑛2𝜕𝑡 𝜙 2 or 𝜇eff, 5 = − 1
Λ𝑛𝜕𝑡𝜙
• Shifts the energy levels between fermions and anti-fermions.
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Dine et. al. (1991) Cohen, Kaplan, Nelson (1991)
𝑙 ,̅ 𝑞�
𝑙, 𝑞
V(ϕ)
ϕ
Scalar VEV Rolls Down
Reheating
Leads to
MAJORANA NEUTRINO Last ingredient: Right-handed neutrino 𝑵𝑹 with Majorana mass term 𝑴𝑹. Motivated by the seesaw mechanism! The processes for 𝚫𝚫 = 𝟐:
• 𝝂𝑳𝒉𝟎 ↔ 𝝂𝑳𝒉𝟎
• 𝝂𝑳𝝂𝑳 ↔ 𝒉𝟎𝒉𝟎
• 𝝂𝑳𝝂𝑳 ↔ 𝒉𝟎𝒉𝟎
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EVOLUTION OF LEPTON ASYMMETRY
𝚲𝐈 = 𝟏.𝟓 × 𝟏𝟎𝟏𝟑 GeV, 𝚪𝑰 = 𝟏𝟎𝟖 GeV, 𝜹𝑹𝑯 = 𝟓 × 𝟏𝟎𝟏𝟐 GeV, and 𝝓𝟎 = 𝟑 × 𝟏𝟎𝟏𝟑 GeV. For 𝝁eff ∝ 𝑴𝒔
−𝟐 case, choose 𝑴𝒔 = 𝟓 × 𝟏𝟎𝟏𝟐 GeV.
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LY, Pearce, Kusenko Phys. Rev. D92 (2015)
Could be the origin of matter-antimatter asymmetry!
SUMMARY • Inflation provides a good solution to the horizon problem,
and explain why the universe is so homogeneous. • Quantum fluctuation of inflaton also provides the seed for
structure formation. • Our electroweak vacuum might not be the true vacuum. • Our universe is now right on the meta-stable region. • Higgs obtains large vacuum expectation during inflation. • The relaxation of the Higgs VEV might be the origin of
matter-antimatter asymmetry. • Higgs relaxation is an important epoch in the early
universe.
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Thanks for your listening!