According to measurements in the last two decades, the expansion of the Universe is accelerating (far Ia supernovae redshifts, WMAP, Planck, ...) pointing to the presence of dark energy (DE). The standard interpretation is relating DE to the cosmological constant lambda. If inflationary scenarii are confirmed, something similar (mutatis mutandi but also with an equation of state p=-rho) occurred shortly after the big bang. However it lasted only from 10-36 to 10-32 s, which is explained e.g. by slow-roll inflation. It is not known whether lambda is constant in time, but what is (are) at all the possible mechanism(s) allowing DE to be present since 13.8 billion years (e.g. in connexion with vacuum energy) ?

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