13.6 Potential applications in cosmology

The systematic deviation of the observed luminosity–red-shift values for type Ia supernovae for large red shift from the expected ones in the standard Friedmann–Robertson–Walker model is usually interpreted as evidence that the expansion of the universe is accelerating. To generate this acceleration, a hypothetical matter field, the dark matter violating the strong energy condition, is postulated. Here the homogeneity and isotropy of the space, i.e., the use of the Friedmann–Robertson–Walker line element, seems to be justified by the isotropy and the thermal nature of the cosmic microwave background radiation. Nevertheless, as is well known, the observed matter distribution is far from being homogeneous. There are huge voids and the matter is distributed as walls between the voids, as in as foam; and hence, the homogeneity of the universe is expected only after an averaging at a larger scale.

However, motivated by quasi-local energy-momentum ideas, Wiltshire [547, 548, 551] suggested a new averaging procedure (see also [550, 549]). Since by general relativistic redshift clocks in the voids run significantly faster than in the presence of matter (i.e., in the walls), the average should be taken in the voids and in the walls separately, and the model of the universe is built from these two like Swiss cheese. Then cosmic acceleration is explained only as an apparent phenomenon, due to the naïve averaging above, in which the general relativistic clock effect was not taken into account, and hence, no dark energy is needed. A well-readable review of the key ideas is [552].

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