Relationship between geometry and expansion rate

[windy miller]

As I understand it, the flatness problem of Bob Dicke, says a flat universe in unstable and so has to be set very precisely in the early universe to give us the flat universe we see today. Is this the same problem as saying the expansion rate had to be finely tuned and if so how are the two related ?

 

[kimbyd]

Flatness is given by the relationship between the density and rate of expansion, with flatness coming from the two being balanced. The prevailing explanation for this is cosmic inflation, which made the universe exponentially flat early-on.

 

[PeterDonis]

the flatness problem of Bob Dicke, says a flat universe in unstable and so has to be set very precisely in the early universe to give us the flat universe we see today

More precisely: a matter-dominated or radiation-dominated universe will move further away from flatness as it expands (unless it happens to have exactly the critical density and be perfectly flat).

Our universe is currently dark energy dominated, so it is (very slowly) moving closer to flatness as it expands (assuming it isn't already perfectly flat).

According to inflation models, our universe was also (effectively) dark energy dominated (the inflaton field acts like dark energy) during inflation, which (rapidly) drove the universe very, very close to flatness, close enough that the period of 10 billion years or so after inflation ended when the universe was radiation and then matter dominated did not move it far enough away from flatness for us to detect the difference.

 

[kimbyd]

More precisely: a matter-dominated or radiation-dominated universe will move further away from flatness as it expands (unless it happens to have exactly the critical density and be perfectly flat).

Our universe is currently dark energy dominated, so it is (very slowly) moving closer to flatness as it expands (assuming it isn't already perfectly flat).

According to inflation models, our universe was also (effectively) dark energy dominated (the inflaton field acts like dark energy) during inflation, which (rapidly) drove the universe very, very close to flatness, close enough that the period of 10 billion years or so after inflation ended when the universe was radiation and then matter dominated did not move it far enough away from flatness for us to detect the difference.

Though even with dark energy, flatness remains a problem early-on. For much of the history of our universe, it was dominated by matter (and earlier, radiation). During this period, the effect of spatial curvature grew by many orders of magnitude. So for it to be observed flat today, it had to be extremely extremely flat early-on, such as when Big Bang Nucleosynthesis was going on.

 

[PeterDonis]

even with dark energy, flatness remains a problem early-on

Yes, that's the issue that inflation models claim to solve.

 

[windy miller]

So my understanding is that the claim that the expansion rate of the universe is delicately fine tuned and the flatness of the geometry is delicately fine tuned is one and the same claim. Is that correct. I am aware that inflation can solve this problem but that is not my questions. Many thanks

 

[PeterDonis]

the claim that the expansion rate of the universe is delicately fine tuned and the flatness of the geometry is delicately fine tuned is one and the same claim

Where have you seen the claim that the expansion rate of the universe is delicately fine tuned?

 

[windy miller]

Where have you seen the claim that the expansion rate of the universe is delicately fine tuned?

Alan Guth says it about 3 minutes into this video
But he is talking about the flatness problem and says the initial expansion rate. So that's what i guess they must be the same thing, are they?