We explore the consequences of allowing non-Hermitian structures in quantum cosmology by extending the Wheeler DeWitt framework beyond strictly Hermitian dynamics. Using a controlled semiclassical reduction, we show how anti Hermitian contributions propagate into both early universe primordial fluctuations and late-time structure growth as effective damping or gain terms. Confronting this framework with inflationary observables, growth of structure and the observed near flatness of the universe, we derive strong infrared constraints that suppress non Hermiticity across cosmic history. We demonstrate that these bounds are mutually consistent between early and late-time probes and can be partially relaxed in theories beyond General Relativity. Our results establish cosmology as a novel arena for testing foundational aspects of quantum mechanics and suggest that Hermiticity may emerge dynamically along the semiclassical branch describing our universe.
We explore the consequences of allowing non-Hermitian structures in quantum cosmology by extending the Wheeler DeWitt framework beyond strictly Hermitian dynamics. Using a controlled semiclassical reduction, we show how anti Hermitian contributions propagate into both early universe primordial fluctuations and late-time structure growth as effective damping or gain terms. Confronting this framework with inflationary observables, growth of structure and the observed near flatness of the universe, we derive strong infrared constraints that suppress non Hermiticity across cosmic history. We demonstrate that these bounds are mutually consistent between early and late-time probes and can be partially relaxed in theories beyond General Relativity. Our results establish cosmology as a novel arena for testing foundational aspects of quantum mechanics and suggest that Hermiticity may emerge dynamically along the semiclassical branch describing our universe.
Introduction Contemporary cosmology includes inflation as one of its central components. It corresponds to a period of accelerated expansion thought to have occurred very early in cosmic history, which takes the universe from relatively generic post Planckian era conditions to a stage where it is well described (with exponential accuracy in the number of e-folds) by a flat Robertson–Walker space-time (which describes a homogeneous and isotropic cosmology). It was initially proposed to resolve various naturalness problems: flatness, horizons, and the excess of massive relic objects, such as topological defects, that were expected to populate the universe according to grand unified theories (GUT). Nowadays, it is lauded because it predicts that the universe's mean density should be essentially identical to the critical value, a very peculiar situation which corresponds to a spatially flat universe. The existing data support this prediction. However, its biggest success is claimed to be the natural account for the emergence of the seeds of cosmic structure in terms of primordial quantum fluctuations, and the correct estimate of the corresponding microwave spectrum. This represents, thus, a situation which requires the combined application of general relativity (GR) and quantum theory, and that, moreover, is tied with observable imprints left from the early universe, in both the radiation in cosmic microwave background (CMB), and in the large scale cosmological structure we can observe today. It should not be surprising that, when dealing with attempts to apply our theories to the universe as a whole, we should come face to face with some of the most profound conceptual problems facing our current physical ideas. In fact, J. Hartle had noted long ago [28] that serious difficulties must be faced when attempting to apply quantum theory to cosmology, although the situations that were envisioned in those early works corresponded to the even more daunting problem of full quantum cosmology, and not the limited use of quantum theory to consider perturbative aspects, which is what is required in the treatment of the inflationary origin of the seeds of cosmic structure. This led him and his collaborators to consider the Consistent Histories framework, which is claimed to offer a version of quantum theory that does not rely on any fundamental notion of measurements, as the favored approach to use in such contexts. We will have a bit more to say about this shortly.
We show that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances and at very early times. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with nonstandard field fluctuations (``quantum nonequilibrium''). We show that inflationary expansion can transfer microscopic nonequilibrium to macroscopic scales, resulting in anomalous power spectra for the cosmic microwave background. The conclusions depend only weakly on the details of the de Broglie-Bohm dynamics. We discuss, in particular, the nonequilibrium breaking of scale invariance for the primordial (scalar) power spectrum. We also show how nonequilibrium can generate primordial perturbations with nonrandom phases and intermode correlations (primordial non-Gaussianity). We address the possibility of a low-power anomaly at large angular scales, and show how it might arise from a nonequilibrium suppression of quantum noise. Recent observations are used to set an approximate bound on violations of quantum theory in the early Universe.
When quantum mechanics was developed in the '20s of the last century another revolution in physics was just starting. It began with the discovery that the universe is expanding. For a long time quantum mechanics and cosmology developed independently of one another. Yet the very discovery of the expansion would eventually draw the two subjects together because it implied the big bang where quantum mechanics wasimportant for cosmology and for understanding and predicting our observations of the universe today. Textbook (Copenhagen) formulations of quantum mechanics are inadequate for cosmology for at least four reasons: 1) They predict the outcomes of measurements made by observers. But in the very early universe no measurements were being made and no observers were around to make them. 2) Observers were outside of the system being measured. But we are interested in a theory of the whole universe where everything, including observers, are inside. 3) Copenhagen quantum mechanics could not retrodict the past. But retrodicting the past to understand how the universe began is the main task of cosmology. 4) Copenhagen quantum mechanics required a fixed classical spacetime geometry not least to give meaning to the time in the Schrödinger equation. But in the very early universe spacetime is fluctuating quantum mechanically (quantum gravity) and without definite value. A formulation of quantum mechanics general enough for cosmology was started by Everett and developed by many. That effort has given us a more general framework that is adequate for cosmology --- decoherent (or consistent) histories quantum theory in the context of semiclassical quantum gravity. Copenhagen quantum theory is an approximation to this more general quantum framework that is appropriate for measurement situations. We discuss whether further generalization may still be required.
Conceptual Problems in Quantum Cosmology The application of quantum theory to cosmology raises a number of conceptual questions, such as the role of the quantum-mechanical notion of “observer” or the absence of a time variable in the Wheeler–DeWitt equation. I point out that a relational formulation of quantum mechanics, and more in general the observation that evolution is always relational, provides a coherent solution to this tangle of problems. A number of confusing issues appear when we try to apply quantum mechanics to cosmology. Quantum mechanics, for instance, is generally formulated in terms of an observer making measurements on a system. In a laboratory experiment, it is easy to identify the system and the observer: but what is the observer in quantum cosmology? Is it part of the same universe described by the cosmological theory, or should we think of it as external to the universe? Furthermore, the basic quantum dynamical equation describing a system including gravity is not the Schrödinger equation, but rather the Wheeler–DeWitt equation, which has no time parameter: is this related to the absence of an observer external to the universe? How do we describe the quantum dynamics of the universe without a time variable in the dynamical equation and without an observer external to the universe? I suggest that clarity on these issues can be obtained by simply recognizing the relational nature of quantum mechanics and more in general the relational nature of physical evolution. In the context of quantum theory, this nature is emphasized by the so-called relational interpretation of quantum mechanics (Rovelli, 1996). The relational nature of evolution, on the other hand, has been pointed out by the partial-observable formulation of general covariant dynamics (Rovelli, 2002). A central observation is that there is a common confusion between two different meanings of the expression “cosmology”. This is discussed below, in Section 15.1.1. A considerable amount of the difficulties mentioned above stems, I argue, from this confusion. The discussion clarifies on the role of the quantum mechanical observer in cosmology, which is considered in Section 15.1.2. In Section 15.2, I briefly describe the relational interpretation of quantum mechanics and some related aspects of quantum theory.
Abstract In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks, yielding, in many cases, quantum bounces. As there is no consensually established boundary condition proposal in quantum cosmology, we investigate the consequences of enlarging known sets of initial wave functions of the Universe, in the specific framework of the Wheeler–DeWitt equation interpreted along the lines of the de Broglie–Bohm quantum theory, on the possible quantum bounce solutions which emerge from them. In particular, we show that many asymmetric quantum bounces are obtained, which may incorporate non-trivial back-reaction mechanisms, as quantum particle production around the bounce, in the quantum background itself. In particular, the old hypothesis that our expanding Universe might have arisen from quantum fluctuations of a fundamental quantum flat space-time is recovered, within a different and yet unexplored perspective.
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.