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13. Kosmologietag, Bielefeld 04.05.2018
μ� [���]
�[���
]
quark-gluonplasma
hadron gas
l = (b)
|l| ≫ b
EVOLUTION OF CHEMICAL
POTENTIALS IN THE EARLY UNIVERSE
Mandy M. Wygas D. Bödeker, I. M. Oldengott, D. J. Schwarz
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
Cosmic QCD Transition
2
Large Lepton Asymmetries
Evolution of Chemical Potentials
LARGE LEPTON ASYMMETRIES INFLUENCE THE COSMIC QCD TRANSITION
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
� ��� ��� ��� ��� ���� �����
��
���
���
���
μ� [���]
�[���
]
criticalpoint?
quark-gluonplasma
hadron gas
liquid-gastransition
3
QCD PHASE DIAGRAM
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
� ��� ��� ��� ��� ���� �����
��
���
���
���
μ� [���]
�[���
]
criticalpoint?
quark-gluonplasma
hadron gas
liquid-gastransition
�l� = �(b)
4
STANDARD EARLY UNIVERSE TRAJECTORY
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
� ��� ��� ��� ��� ���� �����
��
���
���
���
μ� [���]
�[���
]
criticalpoint?
quark-gluonplasma
hadron gas
liquid-gastransition
l = (b)
|l| ≫ b
5
LEPTON ASYMMETRY SHIFTS EARLY UNIVERSE TRAJECTORY
[Schwarz, Stuke, 0906.3434]
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
BARELY ANY CONSTRAINTS ON PRIMORDIAL LEPTON ASYMMETRIES
➤ Specific lepton flavor asymmetry
entropy density,
➤ Constraints only after neutrino flavor oscillations, due to analysis of BBN:
and CMB:
➤ Unequally distributed lepton flavor asymmetries can be equilibrated due to neutrino flavor oscillations
6
l↵ =nL↵
s=
n↵ + n⌫↵
ss
[Mangano, Miele, Pastor, Pisanti, Sarikas,1110.4335]
↵ 2 {e, µ, ⌧}
[Castorina, Franca, Lattanzi, Lesgourgues, Mangano, Melchiorri, Pastor, 1204.2510]
[Barenboim, Kinney, Park, 1609.01584]
[Oldengott, Schwarz,1706.01705]|l| = |3l↵| . 0.02
|le + lµ + l⌧ | ⌘ |l| = |3le| . 0.02
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
CONSERVED CHARGES IN THE EARLY UNIVERSE
➤ Kinetic and chemical equilibrium
➤ For five conserved charges
➤ Specific charge densities:
➤ Corresponding chemical potentials
7
10MeV . T . 100GeV Le, Lµ, L⌧ , B,Q
l↵ =n↵ + n⌫↵
s, ↵ 2 {e, µ, ⌧} ,
b =X
i
bini
s, bi = baryon number of species i ,
q = 0 =X
i
qini
s, qi = charge of species i
µLe , µLµ , µL⌧ , µB , µQ
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
TOY MODEL UNIVERSE HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRY?
8
l
lll
)
net electric charge
+2
But: Universe has to be
charge neutral
lepton asymmetry
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018 9
l
lll
)
net electric charge
+2
But: Universe has to be
charge neutral
Charge has to be compensated by quarks
uu u
d
d dd
u
net electric charge
- 2
Universe is charge neutral
and no baryon asymmetry
)
net baryon number
0
lepton asymmetry
TOY MODEL UNIVERSE HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRY?
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018 10
uu u
d
d dd
u
net electric charge
- 2
Universe is charge neutral
and no baryon asymmetry
)
net baryon number
0
(
quark asymmetries induce
µu, µd
µu =1
3µB +
2
3µQ
µd =1
3µB � 1
3µQ
µB = µu + 2µd
µQ = µu � µd
)
lepton asymmetry induces
baryon chemical potential
TOY MODEL UNIVERSE HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRY?
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRIES?
➤ System of equations:
➤ Unknowns:
11
µLe , µLµ , µL⌧ , µB , µQ
l↵s = n↵ + n⌫↵
bs =X
i
bini
qs = 0 =X
i
qini
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRIES?
➤ System of equations:
➤ Unknowns:
12
➤ free particle net number densities:
➤ divide contribution to quantum number into part by quarks and leptons: µLe , µLµ , µL⌧ , µB , µQ
ni = ni � ni
=gi2⇡2
Z 1
mi
dEEqE2 �m2
i
hnF (E � µi)� nF (E + µi)
inF (E � µi) =
1
e(E�µi) + 1l↵s = n↵ + n⌫↵
bs =X
i
bini
qs = 0 =X
i
qini
l↵s = nlepl↵
= n↵ + n⌫↵
bs = nQCDB
qs = 0 = nQCDQ + nlep
Q = nQCDQ �
X
↵
n↵
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRIES?
➤ System of equations:
➤ Unknowns:
13
➤ free particle net number densities:
➤ :
free leptons, quarks and gluons
➤ :
free leptons & hadron resonance gas approximation
➤ can not account for strong interaction effects around
µLe , µLµ , µL⌧ , µB , µQ
ni = ni � ni
=gi2⇡2
Z 1
mi
dEEqE2 �m2
i
hnF (E � µi)� nF (E + µi)
inF (E � µi) =
1
e(E�µi) + 1
TQCD
T � TQCD
T ⌧ TQCD
l↵s = n↵ + n⌫↵
bs = nQCDB
qs = 0 = nQCDQ �
X
↵
n↵
[Schwarz, Stuke, 0906.3434]
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRIES?
➤ System of equations:
➤ Unknowns:
14
➤ :
Taylor series of the QCD pressure:
➤ Net number densities:
µLe , µLµ , µL⌧ , µB , µQ
l↵s = n↵ + n⌫↵
bs = nQCDB
qs = 0 = nQCDQ �
X
↵
n↵
T ⇠ TQCD
p = �⌦
V= p0 +
1
2!µa�abµb +O(µ4)
�ab = �ba =@2p
@µa@µb
����µ=0
na =@p
@µa= �abµb +O(µ3)
a, b 2 {B,Q}
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRIES?
➤ System of equations:
➤ Unknowns:
15
➤ :
Taylor series of the QCD pressure:
➤ Net number densities:
µLe , µLµ , µL⌧ , µB , µQ
l↵s = n↵ + n⌫↵
bs = nQCDB
qs = 0 = nQCDQ �
X
↵
n↵
T ⇠ TQCD
p = �⌦
V= p0 +
1
2!µa�abµb +O(µ4)
�ab = �ba =@2p
@µa@µb
����µ=0
na =@p
@µa= �abµb +O(µ3)
a, b 2 {B,Q}
) nQCDB = �BQµQ + �BBµB
nQCDQ = �BQµB + �QQµQ
lattice QCD data[Laine, Schröder, 0603048] [HotQCD Collaboration, 1203.0784]
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018 16
EVOLUTION OF BARYON CHEMICAL POTENTIAL - FREE PARTICLES
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018 17
EVOLUTION OF BARYON CHEMICAL POTENTIAL - FREE PARTICLES AND HRG
➤ HRG with resonances up to MeV m 1430[Particle Data Group, (2016) and 2017 update]
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018 18
EVOLUTION OF BARYON CHEMICAL POTENTIAL WITH LATTICE DATA
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018 19
EVOLUTION OF BARYON CHEMICAL POTENTIAL WITH LATTICE DATA
[HotQCD Collaboration, 1203.0784]
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
SUMMARY
➤ Lepton asymmetries poorly constrained
➤ cosmic trajectory through QCD epoch
➤ Large lepton asymmetries may influence the cosmic QCD transition as they induce a larger baryon chemical potential
20
Cosmic QCD Transition | Lepton Asymmetries | Evolution of Chemical Potentials
Mandy M. Wygas - Bielefeld University 13. Kosmologietag, Bielefeld 04.05.2018
SUMMARY
➤ Lepton asymmetries poorly constrained
➤ cosmic trajectory through QCD epoch
➤ Large lepton asymmetries may influence the cosmic QCD transition as they induce a larger baryon chemical potential
21
Thank you!
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