JORGE NORONHA Colloquium at IFT/UNESP, June 2016 Colloquium at IFT/UNESP, June 2016 Weak x strong coupling non-equilibrium dynamics in an expanding universe Based on Phys. Rev. Lett. 116 (2016) 2, 022301, arXiv:1507.07834 [hep-ph] And arXiv:1603.05344 [hep-th]
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JORGE NORONHA
Colloquium at IFT/UNESP, June 2016Colloquium at IFT/UNESP, June 2016
Weak x strong coupling non-equilibrium dynamics in an expanding universe
Based on Phys. Rev. Lett. 116 (2016) 2, 022301, arXiv:1507.07834 [hep-ph]
- This already captures most of the physics we want
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We want to find solutions for the distribution function
Given an initial condition: and
This equation includes general relativistic effects + full nonlinear collision dynamics
How does one solve this type of nonlinear integro-differential equation?
Our Boltzmann equation:
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The moments method
- Originally introduced by Grad (1949) and used by Israel and Stewart (1979) in therelativistic regime.
- Used more recently in Phys. Rev. Lett. 116 (2016) 2, 022301
The idea is simple
Instead of solving for the distribution function itself directly, one uses the Boltzmann eq. to find equations of motion for the moments of the distribution function.
Ex: The particle density is a scalar moment
with equation
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Ex: The energy density is a scalar moment
with equation
Clearly, due to the symmetries, only scalar moments can be nonzero.
Thus, if we can find the time dependence of the scalar moments
via solving their exact equations of motion, one should be able to recover
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It is convenient to define the scale time
(constant mean free path)
And the normalized moments which obey the exact set of eqs:
GR effect Simple recursive nonlinearity
Conservation laws require
PRL 2016, arXiv:1507.07834 [hep-ph]
ALL THE NONLINEAR BOLTZMANN DYNAMICS IS ENCODED HERE
For radiation dominated universe higher order moments will certainly not erase the info about initial conditions.
The approach to equilibrium here depends on the occupancy of each moment.
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Non-equilibrium entropy
One can prove that H-theorem is valid. Entropy production solelyfrom non-hydrodynamic modes.
Even though energy-momentum tensor always the same as in equilibrium.
Expansion is never truly adiabatic.
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This is all very nice but QCD is a non-Abelian gauge theory.
Around the QCD phase transition, QCD is strongly coupled.
Boltzmann description (based on weak coupling) not valid.
How do we study thermalization for T ~ QCD phase transitionin the early universe?
Lattice QCD is useless here (need real time dynamics).
The only thing left to do is to jump into a black hole (brane)
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“Any strongly interacting quantum many-body system at finite density and temperature with sufficiently many d.o.f / volume is predicted to behave at low energies as a perfect fluid”
- The early Universe may be the simplest “way” to study how Standard Modelquantum fields thermalize.
- The perfect fluidity of the early Universe (microsecs after big bang) is an emergingproperty of the Standard Model out-of-equilibrium.
- Exactly solvable nonlinear kinetic models in a FLRW can be studied (led to the1st analytical solution of the Boltzmann equation for expanding gas).
- Due to strong coupling near the QCD phase transition in the early Universe, non-equilibrium dynamics can only be studied using the gauge/gravity duality.
- Toy model of QCD, N=2* gauge theory, behaves as a perfect fluid but thehydrodynamic expansion has zero radius of convergence.
- New ideas are needed to make further progress in this field.