Relationship between geometry and expansion rate

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Discussion Overview

The discussion revolves around the relationship between the geometry of the universe, specifically its flatness, and the expansion rate. Participants explore the implications of the flatness problem, particularly in the context of cosmic inflation and the conditions necessary for a flat universe to exist today.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants describe the flatness problem as indicating that a flat universe is unstable and requires precise initial conditions to maintain flatness over time.
  • There is a proposal that flatness is related to the balance between density and the rate of expansion, with cosmic inflation being a key explanation for achieving flatness early in the universe's history.
  • One participant notes that during a matter-dominated or radiation-dominated phase, the universe tends to move away from flatness unless it has exactly critical density.
  • Another participant emphasizes that the universe's current dark energy dominance is slowly moving it closer to flatness, and that inflation models suggest the universe was effectively dark energy dominated during inflation, which helped achieve near-flatness.
  • Concerns are raised about the flatness problem persisting even with dark energy, suggesting that the universe had to be extremely flat during early epochs, such as during Big Bang Nucleosynthesis.
  • One participant questions whether the claims regarding the delicate fine-tuning of the expansion rate and the flatness of the geometry are equivalent, seeking clarification on this point.
  • Another participant references a video by Alan Guth, suggesting that he connects the initial expansion rate to the flatness problem, prompting further inquiry into whether these concepts are indeed the same.

Areas of Agreement / Disagreement

Participants express varying interpretations of the relationship between the expansion rate and flatness, with some suggesting they are the same issue while others seek clarification. The discussion remains unresolved regarding the equivalence of these claims.

Contextual Notes

Participants reference specific models and concepts, such as cosmic inflation and the effects of dark energy, but the discussion does not reach a consensus on the implications of these ideas for the flatness problem.

windy miller
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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 ?
 
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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.
 
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windy miller said:
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.
 
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PeterDonis said:
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.
 
kimbyd said:
even with dark energy, flatness remains a problem early-on
Yes, that's the issue that inflation models claim to solve.
 
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
 
windy miller said:
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?
 
PeterDonis said:
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?
 

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