  The standard big bang cosmology has been greatly successful in explaining
many observational aspects of the real universe. However, two particular
diffficulties faced by it are the so-called ``horizon'' and ``flatness''
problems. By assuming that the recently found cosmic acceleration to be a
genuine and ever present effect, we show that, the resultant modified Friedman
model is free from both the above referred problems, and there is no need to
invoke the additional ``inflationary'' initial phase as a seperate ingredient.
The important cosmological milestones of the standard big babg cosmology (which
predicts cosmic deceleration) like GUT symmetry breaking epoch or radiation
matter decoupling epoch may remain more or less unchanged in the modified
cosmology in terms of redshift values. However, in terms of cosmic time $t$,
all such epochs occur earlier as the universe becomes older in this case.
