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Correction to: Astrophys Space Sci (2018) 363:13910.1007/s10509-018-3365-3The original article has been updated for copyright reasons with Fig. 1 and a too vague formulation intended to give credit to Farnes (2017) for the originally displayed figure. The sentences “JCM explains the confinement of galaxies and their flat rotation curves, as recently showed by Farnes (2017), see Fig. 1. Mysterious dark matter is no longer required, while the mainstream ΛCDM model does.” have been replaced by “JCM explains the confinement of galaxies and the shape of their rotation curves. As we showed in Petit et al. (2001), if one introduces a surrounding repellent negative matter environment, it gives larger rotation velocities at distance, see Fig. 1. Mysterious dark matter is no longer required, while the mainstream ΛCDM model does.” Figure 1 has been replaced. The figure caption of the earlier Fig. 1 has been replaced by “Fig. 1 Circular velocity, after Petit et al. (2001). This can be compared with results from numerical simulations by Farnes (2017)” The original article has been corrected. [ABSTRACT FROM AUTHOR]

From our exact solution of the Janus Cosmological equation we derive the relation of the predicted magnitude of distant sources versus their red shift. The comparison, through this one free parameter model, to the available data from 740 distant supernovae shows an excellent fit. [ABSTRACT FROM AUTHOR]