The present paradigm, in cosmology is the usual Big-Bang Cosmology in which
two stages of accelerated expansion are incorporated: the inflationary pha
se in the very early universe which produces the classical inhomogeneities
observed in the universe, and a second stage of acceleration at thc, presen
t time as the latest Supernovae observations seem to imply. Both stages cou
ld be produced by a scalar field and observations will strongly constrain t
he microscopic lagrangian, of any proposed model.