Horizon, homogeneity and flatness problems -- do their resolutions really depend upon inflation?

Abstract

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 -- à 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.