Quantum discord in the early universe with non-trivial sound speed

Abstract

Non-trivial sound speed may occur in various interesting scenarios in cosmology and affect the growth of primordial perturbation in the early Universe. This can lead to several observable signatures in the Baryon Acoustic Oscillations, CMB anisotropies, Dark Matter–Baryon Interactions, and the large-scale structure. On the other hand, the vacuum state of curvature perturbation could be expressed as a two-mode squeezed state. In this paper, we study the effects of the non-trivial speed of sound of the perturbations on the evolution of quantum discord for the primordial curvature perturbation using the squeezed formalism. Quantum discord, a measure of the non-classical correlations or quantum correlations between two subsystems of a quantum system, is closely related to the concept of entanglement in the field of quantum information science. We show that the effective speed of sound of primordial perturbations affects the final freeze-in amplitude of the quantum discord. This should provide us with a way to discern the effective speed of sound from quantum discord. We further argue that this may help us further understand the connection between the scrambling time and the effective speed of sounds of the perturbations. These connections can usher a direction when understanding the early Universe from a quantum information point of view.