A model of accelerating dark energy in decelerating gravity

The expansion of the Universe is accelerated as testified by observations of SNeIa at varying redshifts. Explanations of this acceleration are of two kinds: modifications of Einstein gravity or new forms of energy. An example of modified gravity is the braneworld Dvali-Gabadadze-Porrati (DGP) model, an example of dark energy is Chaplygin gas. Both are characterized by a cross-over length scale $r_c$ which marks the transition between physics occurring on our four-dimensional brane, and in a five-dimensional bulk space. Assuming that the scales $r_c$ in the two models are the same, we study Chaplygin gas dark energy in flat DGP geometries. The self-accelerating branch does not give a viable model, it causes too much acceleration. We derive the Hubble function and the luminosity distance for the self-decelerating branch, and then fit a compilation of 192 SNeIa magnitudes and redshifts in the space of the three parameters of the model. Our model with the self-decelerating branch fits the supernova data as successfully as does the $\Lambda CDM$ model, and with only one additional parameter. In contrast to the $\Lambda CDM$ model, this model needs no fine-tuning, and it can explain the coincidence problem. It is unique in the sense that it cannot be reduced to a cosmological constant model in any other limit of the parameter space than in the distant future. If later tests with other cosmological data are successful, we have here a first indication that we live in a five-dimensional braneworld.