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Dark energy from QG in a simple way (Bill Nelson)

  1. Sep 12, 2007 #1


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    It would be really funny if this paper of William Nelson and Mary Sakellariadou turned out to be right. And I can't see any reason it couldn't.

    Dark energy from corrections to the Wheeler-DeWitt equation
    William Nelson, Mairi Sakellariadou (King's College, University of London, U.K.)
    4 pages, 1 figure
    (Submitted on 11 Sep 2007)

    "We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler-DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large scales and that this behaviour is equivalent to additional matter components. This opens up the possibility that dark energy (and possible dark matter) could be large scale manifestations of quantum gravity corrections to classical general relativity. We examine the first order corrections to the Wheeler-DeWitt equation arising from loop quantum cosmology in the absence of lattice refinement and show how the ultimate breakdown in large scale physics occurs."

    the thing is the WHEELER DEWITT EQUATION has been staring everybody in the face for 40 years and apparently nobody noticed before that you could DERIVE DARK ENERGY FROM IT AS A QUANTUM CORRECTION.

    this is a 4 page paper showing how to do that. the standard classical equation for cosmology is the Friedmann (vintage 1923) it is just Einstein plus simplifying assumptions of uniformity and it gives us the familiar expanding universe.
    John Archibald Wheeler and Bryce DeWitt met at Raleigh-Durham Airport for a few hours in 1965 while Wheeler was between planes and there they arrived at a quantized version of Friedmann called the WDW. It was published first in 1967. The WDW is reasonable and close to classical, but it still has the problem that it blows up at the bang singularity. It is an adequate quantum cosmology except right at the singularity point.

    Bryce DeWitt called the equation the "Einstein Schroedinger Equation". Wheeler generously called it the "DeWitt Equation" and everybody else called it WDW. The classical Friedmann scale factor becomes a wave function. So the size of the universe slobbers and gallumphs along like a quantum particle allowing the universe to expand in righteous quantum fashion. And this was over 40 years ago.

    the WDW is what Bojowald's Loop Cosmology quickly converges to as a semiclassical limit a few planck time intervals after the bounce which replaces the bang singularity.
    As Bill and Mary observe, the WDW is what ANY decent QC model converges to, away from where the WDW has singularities and fails to work.

    So this is a very cosmopolitan and ecumenical way to get Dark Energy. Bill and Mary look at the WDW and discover that it yields some QUANTUM CORRECTIONS which they think could explain the observed acceleration in expansion.
    That would be really nice because then you could say that Dark Energy belongs to everybody! It would not belong to any particular Quantum Cosmology. It would belong to ANY QC which converges to the WDW-----it would be generic.

    I should warn that Martin Bojowald in his "Dark Side..." paper earlier this year warned that he suspected this would not work. he said at low curvature the quantum corrections would NOT be enough unless you added small corrections from many many spatial patches together. And he proposed a way to get Dark Energy out of Loop QC which is being published by the CQG journal in its special Dark Energy issue.

    what all these people are discussing are ways of finessing Dark Energy out of QG without any exotic matter or scalar field or any such jazz, just out of the quantum law of gravity itself. they want the acceleration to happen without there BEING any actual dark energy field.

    So here is a possible controversy where Bojowald is saying acceleration happens one way and it looks like Nelson and Sakellariadou say it happens a different way----but in both cases by quantum correction terms in the quantum Friedmann equation.

    this is just my first reaction and I would be happy if someone can correct any error I've made on this. I just put Nelson and Sakellariadou on the biblio thread
    It came as a bit of a surprise.
    Last edited: Sep 12, 2007
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