Metric fluctuations, entropy, and the Wheeler-deWitt equation

Carroll, Robert

doi:10.1007/s11232-007-0076-2

Cited by 12 publications

(13 citation statements)

References 43 publications

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“…( 29) is manifestly scale-invariant, the same must be true for the right hand side, in particular the energymomentum tensor Maeder 2017a), that is, Tµν = T µν . The stress tensor, in general, contains two terms (Carroll 2007) Tµν = T (M)…”

Section: Extension To Cosmologymentioning

confidence: 99%

“…Experiments have also demonstrated that the Corresponding author: G. Gregori gianluca.gregori@physics.ox.ac.uk de Broglie-Bohm trajectories can have a sound physical interpretation if full non-locality is accounted for (Mahler et al 2016). Extensions to quantum fluids (Haas 2011;Cross et al 2014), field theory (Dürr et al 2004;Carroll 2007) and curved space-time (Dürr et al 2014;Holland 1992;Shojai and Shojai 2006) have also been presented.…”

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

Modified Friedmann Equations via Conformal Bohm–de Broglie Gravity

Gregori

Reville

Larder

2019

ApJ

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We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We apply this method to the Robertson-Walker metric to derive a modified version of Friedmann's equations for a Universe consisting of scalar, spinzero, massive particles. These modified equations include additional terms that result from the nonlocal nature of matter and appear as an acceleration in the expansion of the Universe. We see that the same effect may also be present in the case of an inhomogeneous expansion.

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Section: Extension To Cosmologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Modified Friedmann Equations via Conformal Bohm–de Broglie Gravity

Gregori

Reville

Larder

2019

ApJ

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“…e.g. the books and collective volumes) in [3][4][5][6][7][8][9][10][11][12], and individual papers, [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48].…”

Section: G H H H H H H Hmentioning

confidence: 99%

On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

Glinka¹

2014

J Astrophys Aerospace Technol

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The global one-dimensional quantum gravity is the model of quantum gravity which arises from the global onedimensionality conjecture within quantum general relativity, first considered by the author in 2010 and then in 2012. In this model the global dimension is a determinant of a metric of three-dimensional space embedded into an enveloping Lorentizan four-dimensional space-time. In 2012, it has already been presented by the author that this model can be extended to any Lorentzian D + 1-dimensional space-time, where D is a dimension of space, and resulting in the global one-dimensional model of a higher dimensional quantum gravity.The purely quantum-mechanical part of this model is a minimal effective model within the quantum Geometrodynamics, introduced by J.A. Wheeler and B.S. DeWitt in the 1960s, but the effective potential is manifestly different from the one considered by Wheeler & DeWitt. Moreover, in our model the wave functionals solving the quantum gravity are one-variable smooth functions and, therefore, the troublesome mathematical technique of the Feynman functional integration present in the Hawking formulation of quantum gravity, is absent is this model, what makes it a mathematically consistent theory of quantum gravitation.In this paper, we discuss in some detail a certain part of the global one-dimensional model already proposed in 2010, and then developed in 2012. The generalized functional expansion of the effective potential and the residual approximation, which describe the embedded spaces which are maximally symmetric three-dimensional Einstein's manifolds, whose lead to the Newton-Coulomb type potential in the quantum gravity model, are considered. Furthermore, scenarios related to few selected specific forms of the effective potential are suggested as physically interesting and discussed.

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“…[15,16,17,27,34,39,45,49,50,51] and Section 3). There is also a gravitational version of this related to the Wheeler-deWitt (WDW) framework in the form (2.12) [16,17,21,34,51]) and see also [40,92] for WDW). We note also the Perelman entropy functional (2.13)…”

Section: Remarks On Cosmologymentioning

confidence: 99%