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

TL;DR

This paper critically examines the horizon and flatness problems in cosmology, arguing that their traditional formulations depend on assumptions that may not justify the need for inflation, and that flatness is not a falsifiable condition.

Contribution

The authors challenge standard interpretations of the horizon and flatness problems, showing that these issues do not necessarily support inflationary models and are based on assumptions that can be questioned.

Findings

Horizon problem depends on Robertson-Walker assumptions.

Flatness problem is not falsifiable and relies on fine-tuning arguments.

Inflation is not necessarily supported by homogeneity and flatness arguments.

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 -- \`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.