Quantum entanglement in inflationary cosmology

Abstract

We investigate the holographic quantum entanglement of a visible universe in an inflationary cosmology. To do so, we consider an AdS space with a dS boundary which represents an expanding space in time. In an inflationary cosmology, there exists a natural entangling surface called a cosmic event horizon which divides a universe into visible and invisible parts. In this model, cosmic event horizon monotonically decreases and approaches a constant value proportional to the inverse of Hubble constant. We show that the quantum entanglement between the visible and invisible universes divided by cosmic event horizon decreases monotonically in time. After an infinite time evolution, it finally approaches a constant value which is proportional to the inverse square of the Hubble constant for a four-dimensional dS space.

c-theorem of the entanglement entropy

“…In this situation, the AdS/CFT correspondence proposed in the string theory becomes a new and fascinating tool [4][5][6][7], because it enables us to calculate nonperturbatively the entanglement entropy of a strongly interacting quantum system [8][9][10][11][12]. In this work, we investigate the renormalization group (RG) flow of the entanglement entropy and the change of the central charge along the RG flow when a two-dimensional conformal field theory (CFT) is deformed by a relevant operator [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”