## Is the Cosmological Flatness Problem really a problem?

A comment elsewhere on this blog drew my attention to a paper on the arXiv by Marc Holman with the following abstract:

Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called “flatness problem”, which is widely perceived to be a major outstanding problem of modern cosmology and as such forms one of the prime motivations behind inflationary models. An inspection of the literature and some further critical reflection however quickly reveals that the typical formulation of this putative problem is fraught with questionable arguments and misconceptions and that it is moreover imperative to distinguish between different varieties of problem. It is shown that the observational fact that the large-scale Universe is so nearly flat is ultimately no more puzzling than similar “anthropic coincidences”, such as the specific (orders of magnitude of the) values of the gravitational and electromagnetic coupling constants. In particular, there is no fine-tuning problem in connection to flatness of the kind usually argued for. The arguments regarding flatness and particle horizons typically found in cosmological discourses in fact address a mere single issue underlying the standard FLRW cosmologies, namely the extreme improbability of these models with respect to any “reasonable measure” on the “space of all space-times”. This issue may be expressed in different ways and a phase space formulation, due to Penrose, is presented here. A horizon problem only arises when additional assumptions – which are usually kept implicit and at any rate seem rather speculative – are made.

It’s an interesting piece on a topic that I’ve blogged about before. I think it’s well worth reading because many of the discussions of this issue you will find in the literature are very confused and confusing. Apart from mine of course.

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March 30, 2018 at 5:32 am

Ashok Singal also pointed this out. See

https://arxiv.org/abs/1603.01539