Quantum-to-Classical Transition for Fluctuations in the Early Universe

Abstract

According to the inflationary scenario for the very early Universe, all inhomogeneities in the Universe are of genuine quantum origin. On the other hand, looking at these inhomogeneities and measuring them, clearly no specific quantum mechanical properties are observed. We show how the transition from their inherent quantum gravitational nature to classical behavior comes about -a transition whereby none of the successful quantitative predictions of the inflationary scenario for the present-day universe is changed. This is made possible by two properties. First, the quantum state for the spacetime metric perturbations produced by quantum gravitational effects in the early Universe becomes very special (highly squeezed) as a result of the expansion of the Universe (as long as the wavelength of the perturbations exceeds the Hubble radius). Second, decoherence through the environment distinguishes the field amplitude basis as being the pointer basis. This renders the perturbations presently indistinguishable from stochastic classical inhomogeneities. 455 Int. J. Mod. Phys. D 1998.07:455-462. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/21/15. For personal use only.

Classical approximation to quantum cosmological correlations

“…We remark that the problem we are addressing, is related to, but different from the problem of the quantum-to-classical transition [33,34,35,36,37,38], that deals with the way how quantum fluctuations acquire classical properties by decoherence, and with the production of entropy. In this paper we are not investigating how a quantum system evolves to a classical system; we are considering a quantum system and a classical system separately from each other and investigate how well the classical system can reproduce correlation functions of the quantum system.…”

Holographic discreteness of inflationary perturbations

“…The field quanta in the original fluctuations convert to classical perturbations as they pass through the de Sitter-like event horizon; they are then parametrically amplified by an exponential factor during the many subsequent e-foldings of inflation, creating an enormous number of coherent quanta in phase with the original quantum seed perturbation; these in turn create large scale perturbations in the classical gravitational gauge-invariant potential φ m [16], leading to observable anisotropy and large scale structure. All stages of this process are under good calculational control, even the conversion of quantum to classical regimes [17][18][19][20][21][22]. The phase and amplitude of the modes observed today are a direct result of the quantum field activity during inflation; indeed, the hot and and cold spots of microwave anisotropy on the largest scales correspond to faithfully amplified images of the field configurations as they were during inflation.…”

Effective action and decoherence by fermions in quantum cosmology

“…The resulting Euclidean no-boundary wavefunction of fermions reads 13) and, when analytically continued to the complex plane of time τ = π/2H + it, gives exactly the wave function (3.16) that was obtained above by directly solving the Schrödinger equation. The corresponding Lorentzian basis functions…”

“…Then, expanding expression (6.9) in powers of (d − 4) one has the following regularised expression: Substituting (6.10)-(6.12) into (6.9), one has 13) and combining (6.13) with (6.5) one finally has I = 1 − 5 ln 2 2 ln 2 + π 2 8 < 0. (6.14)…”