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arXiv:2401.07662 · Physical review. D/Physical review. D.

Final states in quantum cosmology: Cosmic acceleration as a quantum postselection effect

Charis Anastopoulos

Published Mar 14, 2025• 0 citations
arXivHTMLPDF

Abstract

Standard quantum theory admits naturally statistical ensembles that are both preselected and postselected, i.e., they involve both an initial and a final state. We argue that there is no compelling physical reason to preclude a probability assignment with a final quantum state at the cosmological level. We therefore analyze the implications of a final state in the probability assignment for quantum cosmology. To this end, we derive effective classical equations of motion for systems subject to both initial and final conditions. Remarkably, these effective equations do not depend on the details of the quantum theory, but only on the geometric features of the classical state space. When applied to Friedman-Robertson-Walker cosmological models, these effective equations generically describe cosmic acceleration in the absence of a cosmological constant, dark energy, or modified gravitational dynamics. Therefore, cosmic acceleration emerges as a quantum postselection effect, that is, a macroscopic quantum phenomenon.

DOI
10.1103/physrevd.111.064045

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Standard quantum theory admits naturally statistical ensembles that are both preselected and postselected, i.e., they involve both an initial and a final state. We argue that there is no compelling physical reason to preclude a probability assignment with a final quantum state at the cosmological level. We therefore analyze the implications of a final state in the probability assignment for quantum cosmology. To this end, we derive effective classical equations of motion for systems subject to both initial and final conditions. Remarkably, these effective equations do not depend on the details of the quantum theory, but only on the geometric features of the classical state space. When applied to Friedman-Robertson-Walker cosmological models, these effective equations generically describe cosmic acceleration in the absence of a cosmological constant, dark energy, or modified gravitational dynamics. Therefore, cosmic acceleration emerges as a quantum postselection effect, that is, a macroscopic quantum phenomenon.
The origin of cosmic acceleration remains a central problem in cosmology, commonly attributed to a cosmological constant within the ΛΛΛCDM model or to dynamical dark energy. Here, we develop an alternative approach in which acceleration emerges from quantum post-selection, a standard feature of quantum theory that is not usually incorporated into cosmological modelling. While quantum theory admits both pre-selected and post-selected ensembles, quantum cosmological models are almost exclusively formulated in terms of initial conditions. Building on previous work on post-selected quasiclassical dynamics, we construct a minimal predictive cosmological model in which post-selection and coarse-graining generate effective late-time acceleration without introducing a cosmological constant, dark energy, or modifications of general relativity. The resulting expansion history is highly constrained theoretically and depends on at most two parameters beyond standard Friedmann evolution. Confrontation with type Ia supernova and cosmic chronometer data yields statistically competitive fits while naturally avoiding the coincidence problem. The model also reproduces the standard radiation- and matter-dominated behaviour at early times and predicts a present-day jerk parameter significantly different from the ΛΛΛCDM value. These results suggest that cosmic acceleration may arise as a macroscopic quantum cosmological effect rather than from additional cosmological fluids or modified gravitational dynamics.
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.
The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schrödinger equation complemented by the equations of motion for the momentum operator and its time derivative in Heisenberg's form reduce to the Einstein equations with an additional source of the gravitational field of quantum nature. The spatially closed universe with cosmological constant, originally filled with a uniform scalar field and radiation, is considered as quantum cosmological system. The perfect fluid in the form of radiation defines the material reference frame. The properties of the averaged scalar field which acts like ordinary matter are investigated. After averaging over its quantum states, the free scalar field turns into the Weyssenhoff fluid characterized by the energy density, pressure, and spin of constituent particles. The cases when the contribution of the quantum effects into the gravitational interaction becomes significant on macroscopic scale are analyzed. It is demonstrated that, unless the whole, at least a part of such matter-energy constituents as dark matter and dark energy may have a quantum origin.
The quantized Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model minimally coupled to a free massless scalar field is studied and interpreted in the Bohm-de Broglie framework. We analyze the quantum bohmian trajectories corresponding to a certain class of gaussian packets, solutions of the Wheeler-DeWitt equation. We show that these bohmian trajectories undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period. It is shown that the luminosity-redshift relation in the quantum cosmological model can be made close to the corresponding relation coming from the classical model suplemented by a cosmological constant, for z<1z<1z<1. In this way we have the posibility of interpreting the present observations of high redshift supernovae as the consequence of a quantum cosmological effect.
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a description has a statistical character. Deterministic laws link it to statistical descriptions of the cosmic medium at later times, and because these laws do not privilege any position or direction in space, the same must be true of these descriptions. If the universe is infinite, we can identify the probability that the energy density at a particular instant and a particular point in space (relative to a system of spacetime coordinates in which the postulated spatial symmetries are manifest) lies in a given range with the fractional volume occupied by points where the energy density lies in this range; and similarly with all other probabilities that figure in the statistical description. The probabilities that figure in a complete description of the cosmic medium at any given moment thus have an exact and objective physical interpretation. The statistical entropy and the information associated with each cosmological probability distribution are likewise objective properties of the universe, defined in terms of relative frequencies or spatial averages.
We review the main results that have been obtained in quantum cosmology from the perspective of the de Broglie-Bohm quantum theory. As it is a dynamical theory of assumed objectively real trajectories in the configuration space of the physical system under investigation, this quantum theory is not essentially probabilistic and dispenses the collapse postulate, turning it suitable to be applied to cosmology. In the framework of minisuperspace models, we show how quantum cosmological effects in the de-Broglie-Bohm's approach can avoid the initial singularity, and isotropize the Universe. We then extend minisuperspace in order to include linear cosmological perturbations. We present the main equations which govern the dynamics of quantum cosmological perturbations evolving in non-singular quantum cosmological backgrounds, and calculate some of their observational consequences. These results are not known how to be obtained in other approaches to quantum theory. In the general case of full superspace, we enumerate the possible structures of quantum space and time that emerge from the de Broglie-Bohm picture. Finally, we compare some of the results coming from the de Broglie-Bohm theory with other approaches, and discuss the physical reasons for some discrepancies that occur.