Pointer states for primordial fluctuations in inflationary cosmology

Kiefer, Claus; Lohmar, Ingo; Polarski, David; Starobinsky, Alexei A.

doi:10.1088/0264-9381/24/7/002

Cited by 152 publications

(221 citation statements)

References 62 publications

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“…Equivalently, we see a specific temperature pattern δT (e)/T (no hat) corresponding to the set of numbers a m , see also Eq. (38). In conclusion, the CMB map observed, say, by the WMAP satellite corresponds to one measurement (or one "realization") of the operator δT (e)/T .…”

Section: Ergodicitymentioning

confidence: 87%

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Cosmological inflation and the quantum measurement problem

2012

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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 wavefunction collapse is caused by adding new non linear and stochastic terms to the Schrödinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wavefunction collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schrödinger 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 n S = 4, a spectral index in obvious contradiction with the Cosmic Microwave Background (CMB) 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 has also for 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 rôle to further constrain the CSL parameters. Our results illustrate the remarkable power of inflation and cosmology to constrain new physics.

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Section: Ergodicitymentioning

confidence: 87%

“…According to Eq. (38), measuring the temperature anisotropies is equivalent to measuring the observablesâ m which, in turn, according to Eq. (41), is equivalent to measuring the observablesζ k orv k (that is to sayv…”

Section: Ergodicitymentioning

confidence: 99%

Cosmological inflation and the quantum measurement problem

2012

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“…It is also one of the two conditions which are required for the classicalization of the fluctuations. The second condition is decoherence which is induced by the nonlinearities in the dynamical system which are inevitable since the Einstein action leads to highly nonlinear equatiions (see [69] for a recent discussion of this point, and [70] for related work).…”

Section: Outline Of the Analysismentioning

confidence: 99%

Cosmology of the Very Early Universe

Brandenberger

Dupke²,

Alcaniz³

et al. 2010

AIP Conference Proceedings

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In these lectures I focus on early universe models which can explain the currently observed structure on large scales. I begin with a survey of inflationary cosmology, the current paradigm for understanding the origin of the universe as we observe it today. I will discuss some progress and problems in inflationary cosmology before moving on to a description of two alternative scenariosthe Matter Bounce and String Gas Cosmology. All early universe models connect to observations via the evolution of cosmological perturbations -a topic which will be discussed in detail in these lectures.

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“…We remark that the problem we are addressing, is related to, but different from the problem of the quantum-to-classical transition [33,34,35,36,37,38], that deals with the way how quantum fluctuations acquire classical properties by decoherence, and with the production of entropy. In this paper we are not investigating how a quantum system evolves to a classical system; we are considering a quantum system and a classical system separately from each other and investigate how well the classical system can reproduce correlation functions of the quantum system.…”

Section: Introductionmentioning

confidence: 99%

Classical approximation to quantum cosmological correlations

Meulen¹,

Smit²

2007

J. Cosmol. Astropart. Phys.

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Abstract:We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study φ 3 theory on a de Sitter background for a massless minimally coupled scalar field φ. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale H are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.

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Pointer states for primordial fluctuations in inflationary cosmology

Cited by 152 publications

References 62 publications

Cosmological inflation and the quantum measurement problem

Cosmological inflation and the quantum measurement problem

Cosmology of the Very Early Universe

Classical approximation to quantum cosmological correlations

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