Squeezing of Primordial Gravitational Waves as Quantum Discord

Akira Matsumura,Yasusada Nambu

doi:10.3390/universe6020033

Abstract

We investigate the squeezing of primordial gravitational waves (PGWs) in terms of quantum discord. We construct a classical state of PGWs without quantum discord and compare it with the Bunch–Davies vacuum. Then it is shown that the oscillatory behavior of the angular-power spectrum of the cosmic microwave background (CMB) fluctuations induced by PGWs can be the signature of the quantum discord of PGWs. In addition, we discuss the effect of quantum decoherence on the entanglement and the quantum discord of PGWs for super-horizon modes. For the state of PGWs with decoherence effect, we examine the decoherence condition and the correlation condition introduced by C. Kiefer et al. (Class. Quantum Grav. 24 (2007) 1699). We show that the decoherence condition is not sufficient for the separability of PGWs and the correlation condition implies that the PGWs in the matter-dominated era have quantum discord.

Highlights

In modern cosmology, the early stage of the universe is described by inflation models
We examined the oscillation of the angular-power spectrum of cosmic microwave background (CMB) fluctuations induced by primordial gravitational waves (PGWs)
The dominant contribution of the acoustic oscillation is due to primordial density perturbations not PGWs

Summary

Introduction

The early stage of the universe is described by inflation models. We show that the decoherence condition for the super-horizon modes does not mean the separability of the decohered state of PGWs. We further find that the correlation condition leads to the survival of the quantum discord of PGWs in the matter-dominated era. We have used the Wigner function of the single mode q for the real (or imaginary) part of the field ŷλ to explain the squeezing feature of the state. These two treatments are connected by the following relation ŷRλ (q, η ) = p. Contains the function cq (η ) characterizing the quantum coherence for the modes q and −q

Relation between the Oscillatory Behavior and Quantum Discord

Decoherence for Super-Horizon Modes and Quantum Correlations

Summary