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

Abstract

AbstractThe horizon problem, encountered in cosmology, is derived as such for world models based on Robertson–Walker metric where homogeneity and isotropy of the universe is assumed to begin with and is guaranteed for all epochs. Actually, the only thing that happens in this scenario is that in such a universe, described by a single, time-dependent scale factor, which may otherwise be independent of spatial coordinates, the light signals in a finite time might not cover 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 $$\sim 10^{-35}$$ ∼ 10 - 35 second (near the epoch of inflation) there will be extremely low departures of density from the critical density value (of the order $$\sim 10^{-53}$$ ∼ 10 - 53 ), requiring a sort of fine tuning. We show that even if the present value of the density parameter were very different, still at $$10^{-35}$$ 10 - 35 second it would differ from unity by the same fraction. Thus a use of fine tuning argument to promote $$k = 0$$ k = 0 model amounts to a priori rejection of all models with $$k \ne 0$$ k ≠ 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.