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arXiv:1605.03632 · The European Physical Journal C

Quasi-matter bounce and inflation in the light of the CSL model

Gabriel León, Gabriel R. Bengochea, Susana J. Landau

Published Jul 1, 2016• 11 citations
arXivHTMLPDF

Abstract

The continuous spontaneous localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schrödinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the parameters characterizing the primordial spectra (scalar and tensor), i.e. the amplitude, the spectral index and the tensor-to-scalar ratio. We found that there exist CSL parameter values, allowed by other non-cosmological experiments, for which our predictions for the angular power spectrum of the CMB temperature anisotropy are consistent with the best fit canonical model to the latest data released by the Planck Collaboration.

DOI
10.1140/epjc/s10052-016-4245-z

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The continuous spontaneous localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schrödinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the parameters characterizing the primordial spectra (scalar and tensor), i.e. the amplitude, the spectral index and the tensor-to-scalar ratio. We found that there exist CSL parameter values, allowed by other non-cosmological experiments, for which our predictions for the angular power spectrum of the CMB temperature anisotropy are consistent with the best fit canonical model to the latest data released by the Planck Collaboration.
Cosmic inflation, which describes an accelerated expansion of the early Universe, yields the most successful predictions regarding temperature anisotropies in the cosmic microwave background (CMB). Nevertheless, the precise origin of the primordial perturbations and their quantum-to-classical transition is still an open issue. The continuous spontaneous localization model (CSL), in the cosmological context, might be used to provide a solution to the mentioned puzzles by considering an objective reduction of the inflaton wave function. In this work, we calculate the primordial power spectrum at the next leading order in the Hubble flow functions that results from applying the CSL model to slow roll inflation within the semiclassical gravity framework. We employ the method known as uniform approximation along with a second order expansion in the Hubble flow functions. We analyze some features in the CMB temperature and primordial power spectra that could help to distinguish between the standard prediction and our approach.
The inflationary paradigm is the most successful model that explains the observed spectrum of primordial perturbations. However, the precise emergence of such inhomogeneities and the quantum-to-classical transition of the perturbations has not yet reached a consensus among the community. The continuous spontaneous localization model (CSL), in the cosmological context, might be used to provide a solution to the mentioned issues by considering a dynamical reduction of the wave function. The CSL model has been applied to the inflationary universe before and different conclusions have been obtained. In this letter, we use a different approach to implement the CSL model during inflation. In particular, in addition to accounting for the quantum-to-classical transition, we use the CSL model to generate the primordial perturbations, that is, the dynamical evolution provided by the CSL model is responsible for the transition from a homogeneous and isotropic initial state to a final one lacking such symmetries. Our approach leads to results that can be clearly distinguished from preceding works. Specifically, the scalar and tensor power spectra are not time-dependent, and one retains the amplification mechanism of the CSL model. Moreover, our framework depends only on one parameter (the CSL parameter) and its value is consistent with cosmological and laboratory observations.
Abstract We propose a novel realization for the natural extrapolation of the continuous spontaneous localization (CSL) model, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL model to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory.
We propose a novel model for the natural extrapolation of the continuous spontaneous localization (CSL) theory, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL theory to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory.
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.
We consider the eternal inflation scenario of the slow-roll/chaotic type with the additional element of an objective collapse of the wave function. The incorporation of this new agent to the traditional inflationary setting might represent a possible solution to the quantum measurement problem during inflation, a subject that has not reached a consensus among the community. Specifically, it could provide an explanation for the generation of the primordial anisotropies and inhomogeneities, starting from a perfectly symmetric background and invoking symmetric dynamics. We adopt the continuous spontaneous localization model, in the context of inflation, as the dynamical reduction mechanism that generates the primordial inhomogeneities. Furthermore, when enforcing the objective reduction mechanism, the condition for eternal inflation can be bypassed. In particular, the collapse mechanism incites the wave function, corresponding to the inflaton, to localize itself around the zero mode of the field. Then the zero mode will evolve essentially unperturbed, driving inflation to an end in any region of the Universe where inflation occurred. Also, our approach achieves a primordial spectrum with an amplitude and shape consistent with the one that best fits the observational data.