Horizon, homogeneity and flatness problems -- do their resolutions
  really depend upon inflation?
  We point out that the horizon problem encountered in standard text-books or
review papers on cosmology is, in general, derived for world models based on
Robertson-Walker line element where homogeneity and isotropy of the universe --
\`a la cosmological principle -- is assumed to begin with and is guaranteed for
all epochs. Actually what all happens in that scenario is that in such a
universe, whose evolutionary behaviour is described by a single scale factor,
which may be time dependent but is otherwise independent of spatial
coordinates, the light signals in a finite time might not be covering all the
available space. Further, the flatness problem, as it is posed, is not even
falsifiable. The usual argument offered in the literature is that the present
density of the universe is very close to the critical density value and that
the universe must be flat since otherwise in past at $\sim10^{-35}$ second
(near the epoch of inflation) there will be extremely low departures of density
from the critical density value (of the order $\sim10^{-53}$), requiring a sort
of fine tuning. We show that even if the present value of the density parameter
were very different, still at $10^{-35}$ second it would differ from unity by
the same fraction. Thus a use of fine tuning argument to promote $k = 0$ model
amounts to {\em a priori} rejection of all models with $k \ne 0$. Without
casting any aspersions on the inflationary theory, which after all is the most
promising paradigm to explain the pattern of anisotropies observed in the
cosmic microwave background, we argue that one cannot use homogeneity and
flatness in support of inflation.
