Superhorizon entanglement entropy from particle decay in inflation

Abstract

In inflationary cosmology all particle states decay as a consequence of the lack of kinematic thresholds. The decay of an initial single particle state yields an entangled quantum state of the product particles. We generalize and extend a manifestly unitary field theoretical method to obtain the time evolution of the quantum state. We consider the decay of a light scalar field with mass M ≪ H with a cubic coupling in de Sitter space-time. Radiative corrections feature an infrared enhancement manifest as poles in ∆ = M 2 /3H 2 and we obtain the quantum state in an expansion in ∆. To leading order the pure state density matrix describing the decay of a particle with sub-horizon wavevector is dominated by the emission of superhorizon quanta, describing entanglement between superhorizon and subhorizon fluctuations and correlations across the horizon. Tracing over the superhorizon degrees of freedom yields a mixed state density matrix from which we obtain the entanglement entropy. Asymptotically this entropy grows with the physical volume as a consequence of more modes of the decay products crossing the Hubble radius. A generalization to localized wave packets is provided. The cascade decay of single particle states into many particle states is discussed. We conjecture on possible impact of these results on non-gaussianity and on the "low multipole anomalies" of the CMB.

Time evolution of cascade decay

“…The Wigner-Weisskopf theory of spontaneous emission [28] plays an important role in quantum optics [16][17][18] and in particle physics it is one of the main approaches to study the dynamics of the −K K 0 0 system [29,30] (also −B B 0 0 ). A quantum field theoretical generalization of this important method was provided in [31] with an extension in cosmology in [24,27]. However, to the best of our knowledge the method has not been extended to the case of radiative cascades.…”

“…In inflationary cosmology the rapid expansion of the Universe entails that there is no timelike Killing vector and as a consequence of the lack of kinematic thresholds quanta of a field can decay into quanta of the same field [22][23][24][25][26] leading to the recent suggestion of cascade decay of inflaton quanta during inflation [27] and the concomitant kinematic entanglement of the produced particles.…”

“…For this purpose we provide a non-perturbative quantum field theoretical generalization of the methods ubiquitous in quantum optics [16][17][18][19] adapted to the realm of a full quantum field theory. Furthermore, one of our objectives is to provide a non-perturbative method to study the time evolution directly in real time that would be suitable for applications in cosmology where the expansion of the Universe introduces an explicit time dependence in the evolution Hamiltonian [23,26,27].…”

Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs

“…To date, there have been a number of proposals for holographic theories living in de Sitter space and other cosmological backgrounds [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The purpose of the present paper is to study entanglement generated during the cosmological evolution [29][30][31][32][33][34][35][36][37][38]. Entanglement entropy (or geometric entropy) is an important concept and a useful tool in quantum field theories and quantum many body systems, and serves as a probe to characterize states of matter with long range correlations.…”

Cosmological consequences of initial state entanglement

“…The question of exactly how an entangled initial state might be produced is also a fascinating one and should be investigated further (for some work on entangled states in de Sitter space, see [24,27]). …”