evolution of chemical - physik.uni-bielefeld.de · mandy m. wygas - bielefeld university 13....

13. Kosmologietag, Bielefeld 04.05.2018

μ� [��]

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]

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


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criticalpoint?

quark-gluonplasma

hadron gas

liquid-gastransition

3

QCD PHASE DIAGRAM



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μ� [��]

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criticalpoint?

quark-gluonplasma

hadron gas


�l� = �(b)

4

STANDARD EARLY UNIVERSE TRAJECTORY



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μ� [��]

�[��

]

criticalpoint?

quark-gluonplasma

hadron gas


l = (b)

|l| ≫ b

5

LEPTON ASYMMETRY SHIFTS EARLY UNIVERSE TRAJECTORY

[Schwarz, Stuke, 0906.3434]



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



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



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


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




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




HOW DOES THE BARYON CHEMICAL POTENTIAL DEPEND ON LEPTON ASYMMETRIES?

➤ System of equations:

➤ Unknowns:

11


l↵s = n↵ + n⌫↵

bs =X

i

bini

qs = 0 =X

i

qini





➤ 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↵





➤ 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


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]





➤ Unknowns:

14

➤ :

Taylor series of the QCD pressure:

➤ Net number densities:


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}





➤ Unknowns:

15

➤ :

Taylor series of the QCD pressure:

➤ Net number densities:


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]



EVOLUTION OF BARYON CHEMICAL POTENTIAL - FREE PARTICLES



EVOLUTION OF BARYON CHEMICAL POTENTIAL - FREE PARTICLES AND HRG

➤ HRG with resonances up to MeV m 1430[Particle Data Group, (2016) and 2017 update]



EVOLUTION OF BARYON CHEMICAL POTENTIAL WITH LATTICE DATA



EVOLUTION OF BARYON CHEMICAL POTENTIAL WITH LATTICE DATA

[HotQCD Collaboration, 1203.0784]



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



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!

evolution of chemical - physik.uni-bielefeld.de · mandy m. wygas - bielefeld university 13....

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