Characterizing entanglement entropy produced by nonlinear scalar interactions during inflation

Abstract

The density fluctuations that we observe in the universe today are thought to originate from quantum fluctuations produced during a phase of the early universe called inflation. By evolving a wavefunction describing two coupled Fourier modes of a scalar field forward through an inflationary epoch, we demonstrate that non-linear effects can result in a generation of entanglement entropy between modes with different momenta in a scalar field during the inflationary period when just one of the modes is observed. Through this mechanism, the field would experience decoherence and appear more like a classical distribution today; however the mechanism is not sufficiently efficient to explain classicality. We find that the amount of entanglement entropy generated scales roughly as a power law S ∝ λ 1.75 , where λ is the coupling coefficient of the non-linear potential term. We also investigate how the entanglement entropy scales with the duration of inflation and compare various entanglement measures from the literature with the von Neumann entropy. This demonstration explicitly follows particle creation and interactions between modes; consequently, the mechanism contributing to the generation of the von Neumann entropy can be easily seen.

Superhorizon entanglement entropy from particle decay in inflation

“…Whereas in ref. [80] the entanglement between only two modes was studied in de Sitter space time, ours is a full quantum field theoretical treatment that includes coupling between all modes as befits a local quantum field theory and consistently trace over all the superhorizon degrees of freedom.…”

Quantum entanglement in de Sitter space from stringy axion: An analysis using α vacua

“…It is well accepted fact that von Neumann entropy is a measure of quantum entanglement to quantify long range correlation in condensed matter physics [1][2][3] and cosmology [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In condensed matter physics entanglement entropy exactly mimics the role of an order parameter and the corresponding phase transition phenomena can be characterized by correlations at quantum level.…”

Classical entanglement structure in the wavefunction of inflationary fluctuations

“…Indeed, most large systems undergoing dynamics similar to the form in Eq. (4) are not experiments in laboratories, but rather are natural amplification processes such as the decoherence of macroscopic fields by the nearby medium [89], the decoherence of hydrodynamic variables by the microscopic constituents of a fluid [46,[90][91][92], the decoherence of small particles by ambient radiation [4,18,26,27,93], or the decoherence of the long-wavelength primordial fluctuations by shorter wavelengths (and by other fields and particles) [31,32,39,67,[72][73][74][75]94]. In these naturally occurring examples, the "measured system" is often a collective variable, e.g., the average magnetization of a region, the average pressure within a volume, or the center-of-mass of a macroscopic object.…”

“…We expect that such modifications would induce branching that is similar in most important qualitative ways to the generic case studied here. We refer the reader to [31,[72][73][74][75] for discussions of decoherence from matter self-interactions and other nonminimal couplings, and note that some earlier works [76][77][78] have also studied gravitational interactions.…”