How does inflation drive omega close to 1?

[j9500]

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.

 

[edgepflow]

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.

 

[bapowell]

Physically, you can think of inflation as flattening the universe (which is equivalent to driving omega close to 1). Since spatial curvature scales as 1/a^2(t), where a(t) is the scale factor, the curvature is reduced by the amount of expansion that occurs during inflation. Inflation must satisfy a(t_f) \gtrsim a(t_i)e^{60} and so the spatial curvature is exponentially suppressed.

 

[j9500]

Thanks for your answers. I understand this now, it took me a while to get it, but I have got a handle on it. :)