ИСТИНА

In this work, we study the non-equilibrium dynamics following a local quench in the massive Klein-Gordon theory on curved backgrounds of constant curvature: a space with negative curvature (anti-de Sitter space, AdS) and a space with positive curvature (de Sitter space). We examine excited states of the massive Klein-Gordon field (which, according to holographic duality, are dual to primary operators) in anti-de Sitter and de Sitter spaces, study the dynamics of their correlation functions and the scalar field's energy, and consistently apply holographic duality to such states. Non-trivial contributions to the correlation functions of primary operators in the conformal field theory were obtained, responsible for the non-equilibrium perturbation of the system. We also investigate this dynamics and the applications of duality in the background of a BTZ black hole, whose dual counterpart is a finite-temperature conformal field theory. In de Sitter space, the post-quench dynamics exhibits particle-like perturbations propagating during the early stages of the universe's evolution.