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

TL;DR

This paper explores how a nontrivial sound speed during inflation affects the quantum-information properties of cosmological perturbations, revealing signatures in entanglement and decoherence processes.

Contribution

It introduces a framework to analyze the impact of sound speed on quantum state evolution and diagnostics in inflationary cosmology, with novel numerical regularization techniques.

Findings

Nontrivial sound speed suppresses purity of the reduced quantum state.

It amplifies and modulates entanglement and entropy diagnostics.

A nontrivial sound speed delays the onset of classicality by affecting decoherence.

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 Schr\"odinger evolution of the squeezing parameters ($r_k$ and $\phi_k$). 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, R\'enyi 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.