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Leptogenesis and
Baryogenesis Pasquale Di Bari (University of Southampton) http://www.hep.phys.soton.ac.uk/~pdb1d08
SANGAM@ Harish Chandra Institute, 5-10 March 2018
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Plan
• Lecture I: Cosmological background;
Matter-antimatter asymmetry of the universe
and models of Baryogenesis,
• Lecture II: Neutrino physics and Leptogenesis
• Lecture III: Leptogenesis and BSM physics
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Lecture I
Cosmological background; Matter-antimatter
asymmetry and models of Baryogenesis
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References D.S. Gorbunov, V.A, Rubakov, Introduction to the theory of the early Universe,
World Scientific, 2011
E. Kolb, M. Turner, The early Universe, Addison-Wesley 1993 A.D. Dolgov, Neutrinos in Cosmology, Physics Reports 370 (2002) 333-535
Julien Lesgourgues and Sergio Pastor, Massive Neutrinos and Cosmology,
Physics Reports 429 (2006) 307-379
Scott Dodelson, Modern Cosmology, Academic Press (2003)
Wayne Hu, Scott Dodelson, Cosmic Microwave Background Anisotropies,
Annu.Rev.Astron.Astrophys. 2002.40:171-216
Antonio Riotto, Mark Trodden, Recent progress in Baryogenesis,
hep-ph/9901362
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PDB, A. Masiero, R. Mohapatra editors.,
Focus on the origin of matter, NJP 15 035030:
M. Shaposhnikov et al,
Matter and antimatter in the Universe
D.E.Morrissey and M.J. Ramsey-Musolf,
Electroweak Baryogenesis, arXiv:1206.2942 R. Allahverdi and A.Mazumdar, Affleck-Dine
Baryogenesis, NJP 14, 125013
H.Davoudiasl and R.Mohapatra, On Relating the Genesis of Cosmic Baryons and Dark Matter,
arXiv:1203.1247
PDB, Cosmology and the early universe, CRC Press, 2018.
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Geometry of the Universe
κ=0 κ=+1 κ=-1
Assuming homogeneity and isotropy of space (cosmological principle)
⇒ Friedmann-Robertson-Walker metric (comoving system):
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Cosmological redshift
The wavelength of photons is “stretched by the expansion” !
For photons: ⇒
48
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Hubble’s law from theory
Proper distance ⇒
Expansion rate
Proper velocity
At the present time one can relate the proper distance to the luminosity distance and redshift:
Lemaitre’s equation
!!dpr ,0
Hubble’s law
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Edwin Hubble (1929)
Hubble constant measurements
Hubble Space Telescope Key Project (2001)
110 500~ −− MpcskmH
110 )872( −−±= MpcskmH
Planck 2015 +𝝠CDM
Hubble Space Telescope , Riess et al. (2018)
3.7σ tension
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16
Discovery of gravitational waves to the rescue?
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110 500~ −− MpcskmH
GW170817: The first observation of gravitational waves from from a binary neutron star inspiral
(almost) coincident detection of GW’s and light: one can measure distance from GW’s “sound” and redshift from light: STANDARD SIREN!
A~50 more detections of standard sirens should reduce the error below and solve the current tension between Planck and HST measurements
H0 =70−8+12 km s−1Mpc−1
arXiv:1710.05835
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Fundamental equations of Friedmann cosmology
From the Einstein equations specialized to the FRW metrics: Friedmann equation
Fluid equation
Friedmann equation + Fluid equation
!aa
⎛⎝⎜
⎞⎠⎟
2
≡H2 = 8πG3 ε − ka2R0
2Gµν =8πG Tµν ⇒ Einstein equations
d(εa3)dt
= −pda3
dt⇒ Energy-momentum
tensor conservation
T ;ν
µν =0
⇒ acceleration equation !!a= −4πG(ε +3p)a
Critical energy density
εc ≡3H2
8πG energy density parameter
Ω ≡ ε
εc= ΩXi
i∑
k ≡ H02R0
2(Ω0 −1) ⇒
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Building a cosmological model: general strategy
• Assume an equation of state: p=p(ε)
• Plug the equation of state into the fluid equation
⇒ε = ε(a) • Finally plug ε(a) into the Friedmann equation
⇒ a=a(t) ⇒ε = ε(t)
• Example: Matter universe pM=0 ⇒εM = εM0/a3 ⇒ (flat universe) a(t)= (t/t0)2/3, t0=2H0
-1/3
d(εa3)dt
= −pda3
dt
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Flat Universe with 1 fluid : summary of the results
Matter Universe
equation of state
fluid equation
Friedmann equation
Age of the Universe
Radiation Universe
⇒ if
de Sitter model
energy density vs. time
M
R
p=-ε ω=-1 ε=ε0=const
INFINITE !
ε=ε0=const
Fluids with constant p/ε
(Flat Universe) (Flat Universe) (Flat Universe)
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Matter-radiation equality
From the Einstein equations specialized to the FRW metrics:
p= pM + pR , ε = εM +εR
Consider and admixture of 2 fluids: matter (M) and radiation (R) :
with equations of state:
pM =0, pR =
13εR ,
That, from the fluid equation, lead to :
εM =εM ,0a3
, εR =εR ,0a4
The equality matter-radiation time is defined as:
εM0aeq3 =
εR0aeq4 ⇒ aeq =
εR0εM0
=ΩR0ΩM0
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Friedmann cosmology as a conservative system
From the Einstein equations specialized to the FRW metrics: In terms of H0 and Ω0 the Friedmann equation can be recast as:
!a2
H02 =Ω0
εa2
ε0+(1−Ω0)
If 𝜀 = 𝜀(a) then we can define:
V(a)= −Ω0
εa2
ε0, E0 ≡1−Ω0 ⇒
!a2
H02 +V(a)≡E(a)=E0
Showing that the Friedmann equation has an integral of motion, E(a) , and is, therefore, a conservative system: this will be useful to find the set of solutions for specific models
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Lemaitre models
From the Einstein equations specialized to the FRW metrics: Admixture of 3 fluids: matter (M) + radiation (R) + 𝝠-like fluid (𝝠) :
p= pM + pR + pΛ , ε = εM +εR + εΛ
with equations of state:
pM =0, pR =13εR , pΛ = −εΛ
That, from the fluid equation, lead to :
εM =εM ,0a3
, εR =εR ,0a4
, εΛ =εΛ ,0
⇒ V(a)= −a2 ΩR ,0
a4+ΩM ,0
a3+ΩΛ ,0
⎛
⎝⎜
⎞
⎠⎟
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49
Lemaitre models
E(a)≡ !a
2
H02 +V(a)=E0
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Old results
New results
66
Supernovae type Ia
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The discovery of the cosmic microwave background radiation
Penzias and Wilson (1965)
Tγ0= (3.5 ± 1) 0K
COBE satellite
Tγ0= (2.725 ± 0.002) 0K ⇒ n𝛾0 ≃ 411 cm-3
FIRAS instrument of COBE (1990)
⇒ Ωγ0 ≃ 0.54 × 10-4
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Example: the dipole anisotropy (Δϴ=180∘) corresponds to l =1
COBE DMR microwave map of the sky in Galactic coordinates: temperature variation with respect to the mean value <T> =2.725 K. The color change indicates a fluctuation of ΔT ~ 3.5 mK ⇒ ΔT/T ~ 10-3
100
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COBE (1992) WMAP (2003)
After subtraction of the dipole anisotropy, higher multipole anisotropies are measured with a much lower amplitude than the dipole anisotropy ⇒ T/T ~ 10-5
CMB temperature anisotropies
The angular resolution of COBE was about δΘCOBE 7º , that one of WMAP is 𝜹ΘWMAP 10’ , while that one of Planck is 𝜹ΘPlanck ≃ 3’
99
Planck (2013)
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Acoustic oscillations
99
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Cosmic ingredients (Hu, Dodelson, astro-ph/0110414 )
(Planck 2015, 1502.01589 )
!!ΩB0h2 =0.02222±0.00023
!!ΩCDM ,0h
2 =0.1198±0.0015~5ΩB ,0h2
!Ω0 =1.005±0.005 ΩΛ0 =0.685±0.013
h≡H0
100km s−1 Mpc−1=0.67±0.1
ΩB0 !0.048ΩCDM ,0 !0.26ΩM ,0 !0.308
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Radiation at CMB decoupling
!!Nν
rec =2.94±0.38(Planck 2015, 1502.10589 )
TT+TE+EE+lensing
This proves the presence of neutrinos at recombination and also places a stringent upper bound on the amount of dark radiation ⇒ strong constraints on BSM models But what is the condition for neutrinos to be thermalised?
ΩR0 = Ωγ 0 +Ων0 = gR0
π 2
30T04
εc0!0.27gR0 ×10−4
gR0 = 2+Nν
dec 74Tν0T0
⎛
⎝⎜
⎞
⎠⎟
4
!3.36+ 74(Nνdec −3) Tν0
T0
⎛
⎝⎜
⎞
⎠⎟
4
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58
Flat Radiation-Matter-Λ model
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61
Age of the Universe: in general
a(t)
a0
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61
Age of the universe in the 𝝠CDM model
ΩΛ0 =0.692ΩM0 =0.308H0
−1 =14.4Gyr
t0 =
2H0−1
3 ΩΛ0
ln 1+ ΩΛ0
1−ΩΛ0
⎡
⎣⎢⎢
⎤
⎦⎥⎥!13.8Gyr
t0
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Matter-radiation equality
From the Einstein equations specialized to the FRW metrics:
p= pM + pR , ε = εM +εR
with equations of state:
pM =0, pR =
13εR ,
That, from the fluid equation, lead to :
εM =εM ,0a3
, εR =εR ,0a4
The equality matter-radiation time is defined as:
εM0aeq3 =
εR0aeq4 ⇒ aeq =
εR0εM0
=ΩR0ΩM0
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yrtdec 510 ~
Gyrt 14 ~0
Baryon-to-photon number ratio and recombination
96 Trec
Fractional ionization
Saha equation
Baryon-to-photon number ratio
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Decoupling and recombination Matter and Radiation are coupled until the Thomson scatterings of photons on free electrons are fast enough:
It takes into account the “recombination” of electrons with protons to form Hydrogen athoms,
Expansion of the Universe
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
88
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Matter-radiation equality in numbers
From the Einstein equations specialized to the FRW metrics:
εM0aeq3 =
εR0aeq4 ⇒ aeq =
εR0εM0
=ΩR0ΩM0
= 0.90×10−4
0.31 !2.9×10−4
zeq =1aeq
−1!3400
teq ! teqMΛ
aeqaeqMΛ
⎛
⎝⎜⎜
⎞
⎠⎟⎟
32
≈50,000yr
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
History of The Early Universe
109
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yrtdec 510 ~
Gyrt 14 ~0
The Early Universe is mainly in a radiation dominated regime
~me
110
Number of ultra-relativistic degrees of freedom
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Neutrino decoupling ⇒ relic neutrinos Assume initial thermal equilibrium:
where:
For T< Tνdec neutrinos are decoupled and their number in the comoving volume
remains constant and one expects that at present there is a relic neutrino background together with CMBR with a temperature::
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eVTdec 26.0≅yrtdec 510 ~
Gyrt 14 ~0
Big Bang Nucleosynthesis
At the equilibrium:
Neutrons-protons inter-converting processes
Equilibrium holds until ⇒ Freeze-out
temperature
At the freeze-out:
⇒ ⇒
After the freeze-out neutrons start to decay prior to nucleosynhesis at Life time of neutrons
George Gamow (1904-1968)