Emergence of classicality for primordial fluctuations: Concepts and analogies

Abstract

We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical properties. Two features play an important role in this process: First, the dynamics of fluctuations which are presently on large cosmological scales leads to a very peculiar state (highly squeezed) that is indistinguishable, in a precise sense, from a classical stochastic process. This holds for almost all initial quantum states. Second, the process of decoherence by interaction with the environment distinguishes the field amplitude basis as the robust pointer basis. We discuss in detail the interplay between these features and use simple analogies such as the free quantum particle to illustrate the main conceptual issues.

What does inflation really predict?

“…Figure 10 shows that empirically, by far the most likely way to get large numbers of e-foldings us therefore to roll very little, by having an anomalously small ǫ and hence a tiny roll distance ∆φ. Figure 10 shows that ǫ ∼ (m h /m) 6 at the lowest energies probed, i.e., (ln V ) ′ ∼ (m h /m) 3 , to be contrasted with the expectation (ln V ) ′ ∼ (m h /m) −1 from equation (35). In summary, success requires getting lucky both with ǫ (which happens a fraction ∼ (m h /m) 4 of the time) and with η (which happens a fraction ∼ (m h /m) 2 of the time), which together explains the empirically observed success rate ǫ ∼ (m h /m) 6 .…”

Decoherence: A Closed-System Approach

“…For example, Kiefer and Polarski [72] assume that there is a limit in which f k2 and g k1 (or f k1 and g k2 respectively) behave as…”

“…For this reason Kiefer and Polarski claim "Then the quantum system is effectively equivalent to the classical random system, which is an ensemble of classical trajectories with a certain probability associated to each of them" ( [71] pp. 4) A concrete example in which f k2 and g k1 tend to zero, is the perturbation on de Sitter space [72]. When the decaying mode becomes vanishingly small; when this mode is neglected we are in the limit of a random stochastic process.…”

Untitled

“…One should stress again that the amount of squeezing makes this system extremely peculiar and certainly no laboratory experiment can hope to achieve such huge squeezing. Note that a non relativistic free particle would experience the same transition to a classical stochastic process 16 . In contrast to a free particle, for cosmological perturbations, one is certainly willing to accept the randomness of the fluctuations.…”