How does inflation drive omega close to 1?

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Discussion Overview

The discussion centers around the relationship between cosmic inflation and the parameter omega (Ω), particularly how inflation drives Ω close to 1, indicating a flat universe. The scope includes theoretical explanations and mathematical formulations related to cosmology.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the mechanism by which inflation drives omega close to 1, referencing a statement by Alan Guth.
  • Another participant presents a mathematical equation from "Introduction to Modern Cosmology" by Liddle, suggesting that as time progresses, the exponential term in the equation causes omega to approach 1.
  • A further contribution explains the physical interpretation of inflation as a process that flattens the universe, reducing spatial curvature and leading to omega approaching 1 due to significant expansion during inflation.

Areas of Agreement / Disagreement

Participants appear to agree on the conceptual understanding of inflation's role in driving omega close to 1, but the discussion does not resolve all aspects of the mechanism or implications.

Contextual Notes

The discussion relies on specific mathematical formulations and physical interpretations that may depend on various assumptions about cosmological parameters and the nature of inflation.

j9500
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Hi

I have a question, how does inflation drive omega close to 1? I heard Alan Guth say that inflation drives omega close to 1, how is that so?

I hope I can get an answer for this question, I've been looking for it for quite a while.
 
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In mathematical terms, Equation (13.15) of "Introduction to Modern Cosmology" by Liddle best describes this:

Omega(t) = 1 + exp [ - sqrt (4 * gamma / 3) t ]

Where gamma is the cosmological constant driving inflation.

If Omega(t) = 1, then the universe is flat.

From the above equation, as time elapses, the exponential term vanishes and Omega(t) = 1.
 
Physically, you can think of inflation as flattening the universe (which is equivalent to driving omega close to 1). Since spatial curvature scales as [itex]1/a^2(t)[/itex], where a(t) is the scale factor, the curvature is reduced by the amount of expansion that occurs during inflation. Inflation must satisfy [itex]a(t_f) \gtrsim a(t_i)e^{60}[/itex] and so the spatial curvature is exponentially suppressed.
 
Thanks for your answers. I understand this now, it took me a while to get it, but I have got a handle on it. :)
 

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