Abstract : The ΛCDM standard model, although an excellent parametrization of the present cosmological data, contains two as yet unobserved components, dark matter and dark energy, that constitute more than 95% of the Universe. Faced with this unsatisfactory situation, we study an unconventional cosmology, the Dirac-Milne universe, a matter-antimatter symmetric cosmology, in which antimatter is supposed to present a negative active gravitational mass. The main feature of this cosmology is the linear evolution of the scale factor with time, which directly solves the age and horizon problems of a matter-dominated universe. We study the concordance of this model to the cosmological test of type Ia supernovae distance measurements and calculate the theoretical primordial abundances of light elements for this cosmology. We also show that the acoustic scale of the cosmic microwave background naturally emerges at the degree scale despite an open geometry.