Emergence of classicality for primordial fluctuations: Concepts and analogies

Abstract

Abstract. We clarify the way in which cosmological perturbations of quantum origin, produced during inflation, assume classical prdperties. 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.

Quantum cosmological gravitational waves?

“…( 148), is excluded. Indeed, the squeezing parameter r k would vanish [93]. Note that the purity p k is not constrained by this argument.…”

“…The most famous example of this is probably that a grain of dust whose spatial superposition would be turned into a classical superposition in a fraction of an instant simply by the scattering of photons from the CMB [92]. The importance of decoherence in the discussion of quantum features of cosmological perturbations was quickly realised [93,94]. We now investigate how it affects the state, in general, and in particular the quantum features we have just exhibited.…”

“…Once again, we see that the choice of basis and operators to analyse the state of the system is crucial. For cosmological perturbations, several pointer basis were considered: coherent state basis [96,35], field amplitude basis [97,98,93,94], number basis [97], and others [99] 19 . Ultimately, in a realistic model, the pointer basis is given by the eigenstates of the interaction Hamiltonian selected.…”

“…measures of field amplitude or of number of particles, and also to which operators of the system is the environment sensitive. In their follow-up articles [93,94] to [30], the group of authors (Kiefer, Lesgourgues, Starobinski, Polarski) considered the effect of decoherence. They argued that the correct pointer basis should be the field amplitude basis on the ground that self-interactions of pure gravity are local in the field basis, i.e.…”

“…To start with, how is the level of decoherence of the state estimated? Several criteria have been used in the literature: the so-called rate of de-separation [93], evaluating the suppression of non-diagonal terms [102,101,110], the positivity time if the initial state is assumed to be non-Gaussian [95], δ k [35] or simply the purity p k [107]. We will use the latter since it directly enters our definition of the GHDM (154).…”