MOND-like behavior in the Dirac-Milne universe: Flat rotation curves and mass versus velocity relations in galaxies and clusters

Abstract

Aims. Observational data show that the observed luminous matter is not sufficient to explain several features of the present universe, from gravitational structure formation to the rotational velocities in galaxies and clusters. The mainstream explanation is that the missing mass, although gravitationally active, interacts very weakly with ordinary matter. Competing explanations involve changing the laws of gravity at low accelerations, as in MOdified Newtonian Dynamics (MOND). Here, we suggest that the Dirac-Milne cosmology, a matter-antimatter symmetric cosmology where the two components repel each other, is capable of accounting for such an apparent modification of the Newtonian law, without invoking dark matter. Methods. Using a simple analytical approximation and 1D and 3D simulations, we study rotation curves and virial velocities and compare the mass observed in the simulations to the mass derived assuming Newtonian gravity. Using a modified version of the RAMSES code, we study the Faber-Jackson scaling relation and the intensity of the additional gravitational field created by antimatter clouds. Results. We show that, in the Dirac-Milne universe, rotation curves are generically flat beyond a characteristic distance of ≈2.5 virial radii, and that the Tully-Fisher and Faber-Jackson scaling relations with an exponent ≈3 are satisfied. We show that the mass derived from the rotation curves assuming Newtonian gravity is systematically overestimated compared to the mass really present. In addition, the Dirac-Milne universe, featuring a polarization between its matter and antimatter components, presents a behavior similar to that of MOND, characterized by an additional surface gravity compared to the Newtonian case. We show that in the Dirac-Milne universe, at the present epoch, the intensity of the additional gravitational field gam due to the presence of clouds of antimatter is on the order of a few 10-11 m s-2, similar to the characteristic acceleration of MOND. We study the evolution of this additional acceleration gam and show that it depends on the redshift, and it is therefore not a fundamental constant. Conclusions. Combined with its known concordance properties on the SNIa luminosity distance, age, nucleosynthesis, and structure formation, the Dirac-Milne cosmology may then represent an interesting alternative to the standard cosmological model ΛCDM, MOND, and other scenarios for explaining the dark matter (or missing gravity) and dark energy conundrum.