Why do cosmological perturbations look classical to us? (0810.0087v2)

Abstract: According to the inflationary scenario of cosmology, all structure in the Universe can be traced back to primordial fluctuations during an accelerated (inflationary) phase of the very early Universe. A conceptual problem arises due to the fact that the primordial fluctuations are quantum, while the standard scenario of structure formation deals with classical fluctuations. In this essay we present a concise summary of the physics describing the quantum-to-classical transition. We first discuss the observational indistinguishability between classical and quantum correlation functions in the closed system approach (pragmatic view). We then present the open system approach with environment-induced decoherence. We finally discuss the question of the fluctuations' entropy for which, in principle, the concrete mechanism leading to decoherence possesses observational relevance.

• The paper shows that quantum fluctuations during inflation evolve into classical perturbations as quantum correlations become indistinguishable from classical stochastic averages due to strong squeezing.
• It employs both a pragmatic closed-system approach and environment-induced decoherence to clarify how external interactions suppress quantum interference.
• The findings align with CMB measurements, supporting inflationary models and guiding future research on quantum decoherence in cosmological settings.

Quantum-to-Classical Transition of Cosmological Perturbations

In the paper titled "Why do cosmological perturbations look classical to us?", authors Claus Kiefer and David Polarski explore the conceptual and observational aspects of the quantum-to-classical transition of cosmological perturbations in the context of inflationary cosmology. Their work addresses a crucial area of research: understanding how the quantum fluctuations during inflation evolve into classical structures observed in the present Universe.

Inflationary Cosmology and Perturbation Generation

The framework of inflationary cosmology is central to the understanding of large-scale structure formation in the Universe. Inflation posits that during the early Universe, there was a brief period of accelerated expansion. This inflationary phase sets the stage for quantum fluctuations in the inflaton field, typically described as a massless scalar field satisfying the slow-roll conditions. These fluctuations are pivotal to the generation of cosmological perturbations.

The quantized field dynamics during this phase lead to perturbations that evolve according to quantum field theory principles on a classical curved spacetime background. The authors describe how modes of perturbations, initially sub-Hubble (within the horizon), exit the Hubble radius during inflation due to the accelerated expansion, thus becoming super-Hubble and acquiring particular quantum characteristics, notably squeezing.

Quantum-to-Classical Transition

The authors provide a detailed examination of the quantum-to-classical transition through two primary approaches: the pragmatic view and the environment-induced decoherence perspective.

Pragmatic View

In the pragmatic view or closed-system approach, the authors argue that the classical appearance of perturbations is attributed to the observational indistinguishability between the quantum and classical correlation functions of these perturbations. This view relies on the squeezing of quantum states whereby one aspect (the momentum) becomes negligible, leading to classical random variables effectively representing the field modes.

Quantitatively, the squeezing parameter $r_k$ describes how dominant the classical trajectories become. The enormous squeezing during inflation results in negligible quantum interference between different classical trajectories, ensuring that quantum expectations all but mirror classical stochastic averages.

Environment-Induced Decoherence

The environment-induced decoherence approach complements the pragmatic view, focusing on interactions with external fields or modes (the environment) that lead to decoherence, providing a robust justification for classicality. This interaction results in the loss of quantum coherence, effectively converting pure quantum states into mixed states, or classical ensembles.

The entanglement with the environment also sheds light on the entropy of perturbations. As the Universe evolves, the initial pure state of perturbations develops positive entropy through decoherence, driven by interactions with environmental fields.

Observational Implications

The quantum-to-classical transition has essential implications for understanding the Cosmic Microwave Background (CMB) anisotropies. The power spectrum of primordial fluctuations predicted by inflation can be directly compared with observations of the CMB to validate theoretical models. Observations such as the spectrum's near scale-invariance and the acoustic oscillations are detailed in the paper. These predictions are remarkably consistent with a flat Universe and the structure of adiabatic perturbations observed in the CMB data.

Future Directions and Theoretical Insights

The paper offers a comprehensive exploration of the mechanisms underpinning the quantum-to-classical transition of cosmological perturbations, highlighting both pragmatic and theoretical approaches. The paper calls for continued exploration of quantum decoherence in cosmological settings, examining the role of various initial states and potential environmental interactions.

Future research may expand on these findings, perhaps drawing from quantum gravity theories and deeper engagements with environmental decoherence models, facilitating an even broader understanding of cosmological perturbations and their evolution. Given the ongoing advancements in observational cosmology, such investigations have the potential to refine our grasp of the Universe's origins and its large-scale structure.