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arXiv:2103.01697 · The European Physical Journal C

On the choice of the collapse operator in cosmological Continuous Spontaneous Localisation (CSL) theories

Jérôme Martin, Vincent Vennin

Published Jun 1, 2021• 36 citations
arXivHTMLPDF

Abstract

Abstract The Continuous Spontaneous Localisation (CSL) theory in the cosmological context is subject to uncertainties related to the choice of the collapse operator. In this paper, we constrain its form based on generic arguments. We show that, if the collapse operator is even in the field variables, it is unable to induce the collapse of the wavefunction. Instead, if it is odd, we find that only linear operators are such that the outcomes are distributed according to Gaussian statistics, as required by measurements of the cosmic microwave background. We discuss implications of these results for previously proposed collapse operators. We conclude that the cosmological CSL collapse operator should be linear in the field variables.

DOI
10.1140/epjc/s10052-021-09290-7

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Abstract The Continuous Spontaneous Localisation (CSL) theory in the cosmological context is subject to uncertainties related to the choice of the collapse operator. In this paper, we constrain its form based on generic arguments. We show that, if the collapse operator is even in the field variables, it is unable to induce the collapse of the wavefunction. Instead, if it is odd, we find that only linear operators are such that the outcomes are distributed according to Gaussian statistics, as required by measurements of the cosmic microwave background. We discuss implications of these results for previously proposed collapse operators. We conclude that the cosmological CSL collapse operator should be linear in the field variables.
Abstract In this work we consider a wide variety of alternatives opened when applying the continuous spontaneous localization (CSL) dynamical collapse theory to the inflationary era. The definitive resolution of many of the issues discussed here will have to await, not only for a general relativistic CSL theory, but for a fully workable theory of quantum gravity. Our concern here is to explore these issues, and to warn against premature conclusions. This exploration includes: two different approaches to deal with quantum field theory and gravitation, the identification of the collapse-generating operator and the general nature and values of the parameters of the CSL theory. All the choices connected with these issues have the potential to dramatically alter the conclusions one can draw. We also argue that the incompatibilities found in a recent paper, between the CSL parameter values and the cosmic microwave background observational data, are associated with specific choices made for the extrapolation to the cosmological context of the CSL theory (as it is known to work in non-relativistic laboratory situations) which do not represent the most natural ones.
The inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the continuous spontaneous localization model of wave function collapse in the context of inflation. This modification of quantum dynamics introduces a stochastic nonunitary component to the evolution of the inflaton field perturbations. This leads to passage from a homogeneous and isotropic stage to another, where the quantum uncertainties in the initial state of inflation transmute into the primordial inhomogeneities and anisotropies. We show, by proper choice of the collapse-generating operator, that it is possible to achieve compatibility with the precise observations of the cosmic microwave background radiation.
Models of spontaneous wave function collapse modify the linear Schr\"odinger equation of standard quantum mechanics by adding stochastic nonlinear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such nonlinear terms in the Schr\"odinger equation leads to nonconservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat nonrelativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the well-understood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms, according to the continuous spontaneous localization model, on the standard evolution of nonrelativistic matter and on the formation of cosmic microwave background radiation. We will also put constraints on the continuous spontaneous localization collapse rate $\ensuremath{\lambda}$ by considering that the standard evolution of nonrelativistic matter is not hampered and the observed precise blackbody spectrum of cosmic microwave background radiation would not get distorted (in the form of $\ensuremath{\mu}$-type and yyy-type distortions) so as to violate the observed bounds.
In a recent paper [J. Martin and V. Vennin, Phys. Rev. Lett. 124, 080402 (2020)] it was argued that, for most natural choices, the direct application of the continuous spontaneous localization (CSL) theory to the inflationary case, as it is known to work in non-relativistic laboratory situations, is ruled out by cosmological observational data, thus casting a shadow on models based on CSL theory. We point out that such results are based on the consideration of a rather narrow set of choices for the application of the theory to the cosmological context and that the landscape of open and different possibilities is extremely vast.
According to cosmological inflation, the inhomogeneities in our Universe are of quantum-mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum-to-classical transition, it remains to understand how a specific outcome can be produced in the early Universe, in the absence of any observer. The continuous spontaneous localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wave function collapse is caused by adding new nonlinear and stochastic terms to the Schr\"odinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wave function collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schr\"odinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with nS=4{n}_{\mathrm{S}}=4nS​=4, a spectral index in obvious contradiction with the cosmic microwave background anisotropy observations. The requirement that the non-scale-invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics. Due to the absence of a CSL amplification mechanism in field theory, this also has the consequence that the collapse mechanism of the inflationary fluctuations is not efficient. Then, we determine the collapse time. On small scales the collapse is almost instantaneous, and we recover exactly the behavior of the CSL harmonic oscillator (a case for which we present new results), whereas, on large scales, we find that the collapse is delayed and can take several e-folds to happen. We conclude that recovering the observational successes of inflation and, at the same time, reaching a satisfactory resolution of the inflationary ``macro-objectification'' issue seems problematic in the framework considered here. This work also provides a complete solution to the CSL parametric oscillator system, a topic we suggest could play a very important role to further constrain the CSL parameters. Our results illustrate the remarkable power of inflation and cosmology to constrain new physics.
The hypothesis of the self-induced collapse of the inflaton wave function was introduced as a candidate for the physical process responsible for the emergence of inhomogeneity and anisotropy at all scales. In particular, we consider different proposal for the precise form of the dynamics of the inflaton wave function: (i) the GRW-type collapse schemes proposals based on spontaneous individual collapses which generate nonvanishing expectation values of various physical quantities taken as ansatz modifications of the standard inflationary scenario; (ii) the proposal based on a Continuous Spontaneous Localization (CSL) type modification of the Schrödinger evolution of the inflaton wave function, based on a natural choice of collapse operator. We perform a systematic analysis within the semi-classical gravity approximation, of the standing of those models considering a full quasi-de Sitter expansion scenario. We note that the predictions for the Cosmic Microwave Background (CMB) temperature and polarization spectrum differ slightly from those of the standard cosmological model. We also analyze these proposals with a Bayesian model comparison using recent CMB and Baryonic Acoustic Oscillations (BAO) data. Our results show a moderate preference of the joint CMB and BAO data for one of the studied collapse schemes model over the [Formula: see text]CDM one, while there is no preference when only CMB data are considered. Additionally, analysis using CMB data provide the same Bayesian evidence for both the CSL and Standard Models, i.e. the data have no preference between the simplicity of the LCDM model and the complexity of the collapse scenario.