The flatness problem and the age of the Universe


Most arguments against the problem dispute that there is a fine-tuning problem (i.e. something must have forced Ω to be near 1 in the early universe) and that there is an instability problem (i.e. even if Ω was near 1 in the early universe, it is strange that it is still of order 1 today). (A notable exception is the argument of Lake which demonstrates that if λ is positve and the universe expands forever, then fine-tuning is needed in order to achieve Ω significantly different from one, a reverse of the usual (wrong) argument.) Here, I present another argument, concerning the age of the universe: our universe does not have to be fine-tuned in order to be long-lived; it is long-lived essentially because it is massive. (The usual argument is that if it were not nearly flat, then either it would have collapsed or expanded and thinned out too much before any structure could form.)

One point which I mention, but not in detail, is my view that the coincidence problem is also a non-problem, i.e. that there is an obvious weak-anthropic explanation. In other words, it is equivalent to asking the question why, in a Universe which will expand forever, we are, in some sense, infinitely close to the beginning. That point was quantified by Lineweaver & Egan. Egan & Lineweaver also showed that that holds even in models with dynamic dark energy. I noticed their papers only after writing my paper. (Although I have corresponded with Charley Lineweaver over the years, and met him personally a couple of times, I mention the papers here not because they complained that I should, but rather because they are useful references for my claim.)

This is a pre-copyedited, author-produced version of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The version of record is available at the URLs mentioned on the abstract page, in my publication list, and at the basic-information page for this work.

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