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The Friedmann equation can be written

$$|\Omega-1|=\frac{|k|}{a^2H^2}$$

In a period where the universe is decelerated $a^2H^2$ becomes bigger as we extrapolate into the past.

We know $|\Omega-1|$ is today very close to zero since our universe is pretty flat. But if we extrapolate all the way to the Planck epoch or something like that we would have that $|\Omega-1|\approx 10^{-64}$.

Now for some reason, this is said to pose a fine tuning problem.

But I don't see why this is so. Why can't it just be that $10^{-64}$ is something that simply is?

What do we mean when we say it poses a fine tuning problem?

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  • $\begingroup$ Fine tuning problems are artificial in that they require the assumption that the theory/model that creates them is both correct and complete. There is no good reason to believe that we have such a final and correct model and there is a plethora of suggestions of how this could be extended/replaced in such a way that we can model the current universe from much less restrictive initial conditions (or, better still, no initial conditions, at all, since any such choices merely represent our own ignorance, rather than a property of the universe). $\endgroup$ – CuriousOne May 12 '16 at 2:49
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    $\begingroup$ @CuriousOne - that's why it's a problem. $\endgroup$ – Rob Jeffries May 12 '16 at 5:02
  • $\begingroup$ @RobJeffries: It's a problem to construct a different theory, yes, it's not a problem to explain fine tuning, which doesn't exist. It's a misnomer, if you will. One should call these situations "Dang, my theory just broke!". Unfortunately, especially in the layman literature, this is portrayed as if the theory is fine and we just have to invent intellectual nonsense like multiverses and the anthropic principle to declare that the theory is correct and it's just reality that is broken. $\endgroup$ – CuriousOne May 12 '16 at 7:27
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A fine tuning problem is only a problem if we require that the considered model is a good or complete model of how we think the universe behaves.

In this case, it appears that we require the density of the universe to be as close as 1 part in $10^{64}$ to the exact density that will make it a flat universe that will expand forever, asymptotically coming to rest at $t=\infty$. Yet the model considered (the hot big bang model) makes no prediction of why the density should have this very particular value.

If the density lay outside these bounds then the universe would either have rapidly contracted again into a big crunch, or it would have expanded so much that we would not be able to see other galaxies.

It indicates that we do not have a complete model and that something else is required to give us those initial conditions. This, among other problems, inspired inflationary theory. Or, as you say, we could just stop a search for a more complete theory of why the initial conditions were what they were and just accept that this is the way the universe is?

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