The late-time accelerated expansion of our universe (Perlmutter et al., 1997, 1998, 1999; Riess et al., 1998; Astier et al., 2006) is certainly a major challenge for cosmologists. It will durably affect the way we look at our universe and its future. It is interesting to recall the scientific context in which this accelerated expansion was discovered and promoted to a pillar of the present paradigm. Big Bang cosmology was spectacularly confirmed by the discovery of a remarkably homogeneous cosmic microwave background (CMB) possessing a perfect blackbody spectrum. Nucleosynthesis of the light elements is another of its successes. Important shortcomings of Big Bang cosmology were cured by the introduction of an inflationary stage in the early universe. Inflationary models are constrained by the primordial perturbations they produce, which leave their imprint on the CMB and eventually lead to the formation of cosmic structures through gravitational instability. The inflationary scenario found spectacular support in the detection of the tiny CMB angular anisotropies. These are in agreement with the simplest (single-field slow-roll) inflationary models. In particular, these anisotropies are in agreement with a spatially flat universe, a generic key prediction of inflationary models.
Intererestingly, earlier observations, such as the measurement of cosmic peculiar velocity fields made at the end of the eighties, pointed to a rather low content of dustlike matter, whether dark or baryonic, with Ωm, 0 ≤ 0.3. At that time, this observation was often interpreted as putting the inflationary scenario, despite its beauty and simplicity, in a delicate situation.