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.

5 Responses to “Is the Cosmological Flatness Problem really a problem?”

  1. The “blogged about before” link goes to my comment, not to the top of the blog post. Not that I am complaining. 😐

  2. “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.”

    I agree. I made use of my A4-size iPad Pro to read it in the Alps during the recent (excellent, as always) Moriond cosmology meeting, taking a break from skiing (which, due to the weather and snow conditions, was reputedly excellent) due to major surgery at the beginning of February. Holman’s paper manages to present the discussion clearly without over-simplifying things.

  3. Shantanu Says:

    Ashok Singal also pointed this out. See

    • Has this been published anywhere other than arXiv?

      With regard to the flatness problem, it seems essentially correct, though offering nothing new. I think he misses the point with regard to the horizon problem.

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