Strong-coupling dynamics and entanglement in de Sitter space

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 $$ \mathcal{P} $$ 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.

Holographic evolution with dynamical boundary gravity

“…We use the same model as in ref. [14], to which we refer the reader for additional details. The four-dimensional gauge theory is a large-N , strongly coupled, non-conformal theory with a mass scale M .…”

“…For example, this metric is flat in the holographic description of the quark-gluon plasma [1,2] or in applications to condensed matter systems [3][4][5]. Applications with a curved metric include gauge dynamics in black hole backgrounds [6] or in de Sitter (dS) space [7][8][9][10][11][12][13][14]. In all these cases the boundary metric influences, but is unaffected by, the gauge theory dynamics.…”

Spinodal Gravitational Waves

“…If the phase transition takes place in a hidden sector that is reacting to, but not affecting the, expansion of the Universe, then this would amount to fixing the boundary metric to be time-dependent but not dynamical, as in e.g. [55][56][57][58][59][60][61][62]. If the transition takes place in the sector driving the expansion of the Universe, then a more rigorous calculation should include the backreaction of the degrees of freedom undergoing the transition on the spacetime metric, along the lines of [63].…”

Domain collisions

“…Holography has provided numerous insights into the out-of-equilibrium properties of hot, strongly-coupled, non-Abelian plasmas [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][22][23][24][25][26][27][28][29][30][31][32][33] (see e.g. [34] for a review).…”