Quantum-information diagnostics of cosmological perturbations with nontrivial sound speed in inflation

Abstract

In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schrödinger evolution of the squeezing parameters ($r_k$ and ${\varphi }_k$). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, Rényi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable $x=\tanh r_k$ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.

Comments: 33 pages, 5 figures