Thermalization in Quenched Open Quantum Cosmology

TL;DR

This paper investigates quantum thermalization in a curved spacetime setting, specifically de Sitter space, using a quenched open quantum field model and analyzing two-point correlation functions to understand the thermalization process.

Contribution

It extends the Caldeira-Leggett model to curved spacetime, derives the gCC state post-quench in de Sitter space, and explores the effects of initial states on thermalization and power spectra.

Findings

Subsystems thermalize in de Sitter space regardless of initial state.

Explicit form of two-point correlators showing thermalization process.

Identification of conserved charges related to $W_{}$ algebra in this context.

Abstract

In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of $W_{\infty}$ algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.