How Problematic is the NearEuclidean Spatial Geometry of the LargeScale Universe?
Abstract
Modern observations based on general relativity indicate that the spatial geometry of the expanding, largescale Universe is very nearly Euclidean. This basic empirical fact is at the core of the socalled "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 largescale 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 finetuning 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 spacetimes". 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.
 Publication:

Foundations of Physics
 Pub Date:
 November 2018
 DOI:
 10.1007/s1070101802184
 arXiv:
 arXiv:1803.05148
 Bibcode:
 2018FoPh...48.1617H
 Keywords:

 Cosmological flatness problem;
 General relativity;
 FLRW solutions;
 Initial conditions;
 Finetuning;
 Inflation;
 Horizon problem;
 Second law of thermodynamics;
 Quantum gravity;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 25 pages, 2 figures. Minor revisions for published version