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On the nature of dark energy: the lattice Universe


There is something unknown in the cosmos. Something big. Which causes the acceleration of the Universe expansion, that is perhaps the most surprising and unexpected discovery of the last decades, and thus represents one of the most pressing mysteries of the Universe. The current standard ΛCDM model uses two unknown entities to make everything fit: dark energy and dark matter, which together would constitute more than 95 % of the energy density of the Universe. A bit like saying that we have understood almost nothing, but without openly admitting it. Here we start from the recent theoretical results that come from the extension of general relativity to antimatter, through CPT symmetry. This theory predicts a mutual gravitational repulsion between matter and antimatter. Our basic assumption is that the Universe contains equal amounts of matter and antimatter, with antimatter possibly located in cosmic voids, as discussed in previous works. From this scenario we develop a simple cosmological model, from whose equations we derive the first results. While the existence of the elusive dark energy is completely replaced by gravitational repulsion, the presence of dark matter is not excluded, but not strictly required, as most of the related phenomena can also be ascribed to repulsive-gravity effects. With a matter energy density ranging from ∼5 % (baryonic matter alone, and as much antimatter) to ∼25 % of the so-called critical density, the present age of the Universe varies between about 13 and 15 Gyr. The SN Ia test is successfully passed, with residuals comparable with those of the ΛCDM model in the observed redshift range, but with a clear prediction for fainter SNe at higher z. Moreover, this model has neither horizon nor coincidence problems, and no initial singularity is requested. In conclusion, we have replaced all the tough problems of the current standard cosmology (including the matter-antimatter asymmetry) with only one question: is the gravitational interaction between matter and antimatter really repulsive as predicted by the theory and as the observation of the Universe seems to suggest? We are awaiting experimental responses.

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  1. The geodesic equation for a massless particle, such as a photon, is formally equal to Eq. (7), except for the parameter s, which can no longer be taken as the proper time, being \({\rm d}s=0\), but it will be an affine parameter describing the world line. Thus, a (retarded) photon will be repelled by an antimatter-generated gravitational field, and a CPT-transformed photon, i.e. an advanced photon, will be repelled by matter.

  2. Previous studies on a matter-antimatter symmetric Universe (e.g. Cohen et al. 1998) seemed to exclude the possibility that matter and antimatter domains have sizes smaller than the visible Universe, due to the lack of the expected annihilation radiation from the domain boundaries, but, unlike in those models, in our scenario annihilation is prevented by gravitational repulsion, so that such a lower limit is no longer valid.

  3. This simile between ionic crystals and Universe structure can also be found in Ripalda (2010).

  4. Although observations seem to favor k=0, a negatively curved space can not be excluded (see e.g. Benoit-Lévy and Chardin 2012).


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Correspondence to M. Villata.

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Villata, M. On the nature of dark energy: the lattice Universe. Astrophys Space Sci 345, 1–9 (2013).

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  • Cosmology: theory
  • Dark energy
  • Gravitation
  • Large-scale structure of Universe