Abstract
After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.
Highlights
IntroductionLong before the 1996 popular paper [1] by Polarski and Starobinsky (PS) on cosmological decoherence which commanded the attention of the cosmology community, there had already been intense activities on the issue of quantum decoherence: two major paradigms of consistent/decoherent histories [2,3,4,5,6,7,8,9] and the environment-induced decoherence [10,11,12,13,14]
The main goal of this paper is to focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when one does not rely on an environment
With a mixed variable coming from classical gravity and quantum field, what do quantum cosmological perturbations refer to, and which variables are we targeting in their decoherence, or, which quantum variables become classical at late times—or do they?
Summary
Long before the 1996 popular paper [1] by Polarski and Starobinsky (PS) on cosmological decoherence which commanded the attention of the cosmology community, there had already been intense activities on the issue of quantum decoherence: two major paradigms of consistent/decoherent histories [2,3,4,5,6,7,8,9] and the environment-induced decoherence [10,11,12,13,14]. The main goal of this paper is to focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when one does not rely on an environment This is what ‘intrinsic’ in the title refers to—a closed system. The issue of decoherence for a free field is perhaps conceptually more challenging, not unlike defining the ‘intrinsic’ entropy of a quantum field (see, e.g., [31] and earlier references cited therein) This is because, if one adheres to the basic principles, a closed quantum system should evolve unitarily—there is no loss of quantum coherence. The contrast with PS is even clearer: while PS asserted that there is decoherence with a clever twist, we show that there is no decoherence, and no twist
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
