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!