Dark Energy
‘Dark energy’ is the name introduced by Mike Turner, for what had been called the ‘Λ term’, or ‘cosmological term’ in Einstein’s field equations for more than half a century, a term that had no obvious physical meaning – at least not in the laboratory – but that could not be rejected either from the cosmological field equations if one was looking for the most general second-order equations derivable from a scalar Lagrangean. During the last decade, measurements with increasing accuracy of the present average cosmic expansion signalled an increasing expansion rate of the substratum – an acceleration – in obvious violation of energy conservation: An expanding cloud of self-gravitating objects should decelerate. This misbehaviour of cosmological kinematics urged Turner to introduce his cryptic – and even somewhat misleading – name ”dark energy” for the Λ-term: Λ does not correspond to an energy density because it exerts a negative pressure, forbidden by the classical energy inequalities for laboratory substance (e.g. Kundt 1972); it is a non-energy, or at best a quasi-energy.
For this reason, it struck me as a salvation of (serious) cosmology when I read about David Wiltshire’s dismissing dark energy (Wiltshire 2007a,b, Ellis 2008). His thesis is simple and convincing: Cosmology had hitherto been evaluated wrongly, by ignoring the inhomogeneous distribution of its substratum. We know Shapiro’s ‘time delay’ effect in the solar system, and in close neutron-star binaries: Signals passing close to heavy objects (stars, galaxies) reach a distant observer with a certain delay. In the same vein, when we measure cosmic expansion, we use light rays which have propagated through an inhomogenous Universe, with voids and walls, sometimes propagating through near- vacuum patches (voids), and sometimes skimming heavy mass concentrations (clusters of galaxies, in the walls). Clearly, the formulae derived for a homogeneous cosmological model cannot be expected to describe our observations correctly, due to non-linearities. Our local time scale, described by our (timelike) worldline, inside our (massive) Galaxy, has to be referred to the average cosmic timescale via intersections with successive null geodesics lying on past light cones, and connecting us to distant sources in the past. There is no a priori reason why these two timescales should be the same. A deviation is expected, an acceleration, whose sign we must calculate, and whose magnitude must likewise be calculated. It is a cumulative effect, to be obtained by integration over large spacetime distances. Wiltshire has done such calculations, and claims that their result describes the observed seemingly accelerated expansion, without a Λ-term in the field equations. All we have to do is evaluate our observations rigorously.
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