Abstract
We use holography to study the dynamics of a strongly-coupled gauge theory in four-dimensional de Sitter space with Hubble rate H. The gauge theory is non-conformal with a characteristic mass scale M. We solve Einstein’s equations numerically and determine the time evolution of homogeneous gauge theory states. If their initial energy density is high compared with H4 then the early-time evolution is well described by viscous hydrodynamics with a non-zero bulk viscosity. At late times the dynamics is always far from equilibrium. The asymptotic late-time state preserves the full de Sitter symmetry group and its dual geometry is a domain-wall in AdS5. The approach to this state is characterised by an emergent relation of the form mathcal{P} = w ℰ that is different from the equilibrium equation of state in flat space. The constant w does not depend on the initial conditions but only on H/M and is negative if the ratio H/M is close to unity. The event and the apparent horizons of the late-time solution do not coincide with one another, reflecting its non-equilibrium nature. In between them lies an “entanglement horizon” that cannot be penetrated by extremal surfaces anchored at the boundary, which we use to compute the entanglement entropy of boundary regions. If the entangling region equals the observable universe then the extremal surface coincides with a bulk cosmological horizon that just touches the event horizon, while for larger regions the extremal surface probes behind the event horizon.
Highlights
The fireball expands, cools down and eventually hadronises
Another interesting scenario comes from the possibility that the physics beyond the Standard Model might be completed at some high-energy scale by a Grand Unified non-Abelian gauge Theory (GUT)
We have carefully explained the holographic renormalisation of the model and the anomalies that arise in the dual field theory due to the curved boundary geometry and the scalar field
Summary
The fireball expands, cools down and eventually hadronises. In QCD in equilibrium, this transition is realised as a smooth crossover [6]. One motivation comes from Cosmology, where the dynamics of the gauge theory is coupled to an expanding spacetime. This situation was certainly realised about one microsecond after the Big Bang, when the decreasing temperature of the Universe crossed the QCD critical temperature and quarks and gluons became bound into hadrons. Another interesting scenario comes from the possibility that the physics beyond the Standard Model might be completed at some high-energy scale by a Grand Unified non-Abelian gauge Theory (GUT). These include the fact that at late times the apparent and the event horizons do not coincide, reflecting the non-equilibrium nature of the state, or the existence of an entanglement horizon in between them that cannot be penetrated by extremal surface anchored at the boundary
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