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arXiv:1510.02523

Statistical anisotropy and cosmological quantum relaxation

Antony Valentini

Published Oct 8, 2015• 9 citations
arXivHTMLPDF

Abstract

We show that cosmological quantum relaxation predicts an anisotropic primordial power spectrum with a specific dependence on wavenumber k. We explore some of the consequences for precision measurements of the cosmic microwave background (CMB). Quantum relaxation is a feature of the de Broglie-Bohm pilot-wave formulation of quantum theory, which allows the existence of more general physical states that violate the Born probability rule. Recent work has shown that relaxation to the Born rule is suppressed for long-wavelength field modes on expanding space, resulting in a large-scale power deficit with a characteristic inverse-tangent dependence on k. Because the quantum relaxation dynamics is independent of the direction of the wave vector for the relaxing field mode, in the limit of weak anisotropy we are able to derive an expression for the anisotropic power spectrum that is determined by the power deficit function. As a result, the off-diagonal terms in the CMB covariance matrix are also determined by the power deficit. We show that the lowest-order l-(l+1) inter-multipole correlations have a characteristic scaling with multipole moment l. Our derived spectrum also predicts a residual statistical anisotropy at small scales, with an approximate consistency relation between the scaling of the l-(l+1) correlations and the scaling of the angular power spectrum at high l. We also predict a relationship between the l-(l+1) correlations at large and small scales. Cosmological quantum relaxation appears to provide a single physical mechanism that predicts both a large-scale power deficit and a range of statistical anisotropies, together with potentially testable relationships between them.

DOI
10.48550/arxiv.1510.02523

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We show that cosmological quantum relaxation predicts an anisotropic primordial power spectrum with a specific dependence on wavenumber k. We explore some of the consequences for precision measurements of the cosmic microwave background (CMB). Quantum relaxation is a feature of the de Broglie-Bohm pilot-wave formulation of quantum theory, which allows the existence of more general physical states that violate the Born probability rule. Recent work has shown that relaxation to the Born rule is suppressed for long-wavelength field modes on expanding space, resulting in a large-scale power deficit with a characteristic inverse-tangent dependence on k. Because the quantum relaxation dynamics is independent of the direction of the wave vector for the relaxing field mode, in the limit of weak anisotropy we are able to derive an expression for the anisotropic power spectrum that is determined by the power deficit function. As a result, the off-diagonal terms in the CMB covariance matrix are also determined by the power deficit. We show that the lowest-order l-(l+1) inter-multipole correlations have a characteristic scaling with multipole moment l. Our derived spectrum also predicts a residual statistical anisotropy at small scales, with an approximate consistency relation between the scaling of the l-(l+1) correlations and the scaling of the angular power spectrum at high l. We also predict a relationship between the l-(l+1) correlations at large and small scales. Cosmological quantum relaxation appears to provide a single physical mechanism that predicts both a large-scale power deficit and a range of statistical anisotropies, together with potentially testable relationships between them.
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We present arguments suggesting that deviations from the Born probability rule could be generated for trans-Planckian field modes during inflation. Such deviations are theoretically possible in the de Broglie-Bohm pilot-wave formulation of quantum mechanics, according to which the Born rule describes a state of statistical equilibrium. We suggest that a stable equilibrium state can exist only in restricted conditions: on a classical background spacetime that is globally hyperbolic or in a mild quantum-gravity regime in which there is an effective Schrödinger equation with a well-defined time parameter. These arguments suggest that quantum equilibrium will be unstable at the Planck scale. We construct a model in which quantum nonequilibrium is generated by a time-dependent regulator for pilot-wave dynamics, where the regulator is introduced to eliminate phase singularities. Applying our model to trans-Planckian modes that exit the Planck radius, we calculate the corrected primordial power spectrum and show that it displays a power excess (above a critical wavenumber). We briefly consider how our proposals could be tested by measurements of the cosmic microwave background.