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Using Bell Experiments to Test the Quantumness of Primordial Fluctuations

Junqi Wang

Published Jan 1, 2025• 0 citations
Publisher

Abstract

The primordial fluctuations during inflation are widely believed to seed the Large Scale Structure of the universe. However, it remains unknown whether these fluctuations have a quantum nature. According to the inflation theory, the expanding universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Therefore, cosmological Bell inequalities are well motivated and can be formulated using pseudo-spin operators, constructed from operators involving the momenta of the fluctuations. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. However, the cosmological Bell test faces several obstructions, including decoherence and the fast-decaying momenta. We thus study the Bell test on scalar modes and tensor modes with decoherence from the interactions of cosmological perturbations, including the bulk and boundary interaction terms. We explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test. We also discuss the possibility of constructing Bell tests for the entanglement between polarizations, which may avoid the fast-decaying momenta problem and be another way, besides the tabletop experiments and large gravitational waves detectors, to test the quantum nature of gravity.

DOI
10.14711/thesis-hdl152381

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The primordial fluctuations during inflation are widely believed to seed the Large Scale Structure of the universe. However, it remains unknown whether these fluctuations have a quantum nature. According to the inflation theory, the expanding universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Therefore, cosmological Bell inequalities are well motivated and can be formulated using pseudo-spin operators, constructed from operators involving the momenta of the fluctuations. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. However, the cosmological Bell test faces several obstructions, including decoherence and the fast-decaying momenta. We thus study the Bell test on scalar modes and tensor modes with decoherence from the interactions of cosmological perturbations, including the bulk and boundary interaction terms. We explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test. We also discuss the possibility of constructing Bell tests for the entanglement between polarizations, which may avoid the fast-decaying momenta problem and be another way, besides the tabletop experiments and large gravitational waves detectors, to test the quantum nature of gravity.
Abstract The inflationary universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Operators involving the momenta of the fluctuations can be rewritten into pseudo-spin operators, such as the Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin operators, cosmological Bell inequalities can be formulated. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations. In this work, we focus on primordial curvature perturbations. Since curvature perturbations arise from gravity, their action includes the Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in selecting suitable initial conditions for linear perturbations. After that, we proceed to the interactions of cosmological perturbations, including the bulk and boundary interaction terms, which introduce decoherence effects. These decoherence effects change the expectation value of the Bell operator, and gradually restore the Bell inequality. We describe this process by a “Bell test curve”, which offers a window around 5 e-folds for testing the quantum origin of cosmological perturbations. We also explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test curve.
Inflationary cosmology successfully accounts for the observed properties of primordial fluctuations using quantum field theory in an expanding background. However, the quantum nature of these fluctuations has not been experimentally established, since classical stochastic models could reproduce the observed two-point statistics by construction. Existing approaches to testing primordial quantumness focus primarily on Bell inequalities, which provide a sharp conceptual criterion but are difficult to implement with cosmological observables. In this work we adopt a falsification-based approach. We define a precise classical hypothesis for the origin of primordial perturbations (local stochastic fields admitting a positive probability distribution) and identify inequality constraints that must be satisfied within this class. We show how violations of these classicality inequalities can be probed using realistic cosmological observables, without invoking Bell tests or non-commuting measurement settings. We further identify symmetry-protected spectator sectors in which quantum coherence is parametrically preserved during inflation, allowing violations of observable magnitude to survive decoherence. Our results show that large-scale structure and future 21 cm surveys provide a viable and quantitative route to falsifying classical stochastic descriptions of primordial fluctuations.
One of the cornerstones of inflationary cosmology is that primordial density fluctuations have a quantum mechanical origin. However, most physicists consider that such quantum mechanical effects disappear in CMB data due to decoherence. In this conference report, we show that the violation of Bell inequalities in an initial state of our universe increases exponentially with the number of modes to measure in inflation. This indicates that some evidence that our universe has a quantum mechanical origin may survive in CMB data, even if quantum entanglement decays exponentially afterward due to decoherence.
We present a general and systematic study of how a Bell experiment on the cosmic microwave background could be carried out. We introduce different classes of pseudo-spin operators and show that, if the system is placed in a two-mode squeezed state as inflation predicts, they all lead to a violation of the Bell inequality. However, we also discuss the obstacles that one faces in order to realize this program in practice and show that they are probably insurmountable. We suggest alternative methods that could reveal the quantum origin of cosmological structures without relying on Bell experiments.
Abstract Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as cosmological density fluctuations. In this work, we show how Bell operators can be constructed for quantum fields in real space, and for Gaussian states we compute their expectation value in terms of the field power spectra. We then apply our formalism to a scalar field in de-Sitter space-time. We find that, in spite of the tremendous production of entangled particles with opposite wave momenta on large scales, Bell inequalities are not violated in real space. The reason is that, when considering measurements of a field at two distinct locations in real space, one implicitly traces over the configuration of the field at every other location, leading to a mixed bipartite system. This “effective decoherence” effect is responsible for the erasure of quantum features, and casts some doubts on our ability to reveal the quantum origin of cosmological structures. We finally discuss these results in the light of quantum discord.
According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave—CMB—anisotropy…) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether astrophysical observations could unambiguously reveal this quantum origin by borrowing ideas from quantum information theory. It is argued that some of the tools needed to carry out this task have been discussed long ago by J. Bell in a, so far, largely unrecognized contribution. A detailled study of his paper and of the criticisms that have been put forward against his work is presented. Although J. Bell could not have realized it when he wrote his letter since the quantum state of cosmological perturbations was not yet fully characterized at that time, it is also shown that Cosmology and cosmic inflation represent the most interesting frameworks to apply the concepts he investigated. This confirms that cosmic inflation is not only a successful paradigm to understand the early Universe. It is also the only situation in Physics where one crucially needs General Relativity and Quantum Mechanics to derive the predictions of a theory and, where, at the same time, we have high-accuracy data to test these predictions, making inflation a playground of utmost importance to discuss foundational issues in Quantum Mechanics.