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## Main Question or Discussion Point

Hi, I'm totally lost on how inflation solves the horizon and flatness problem.

d/dt(1/Ha)<0

and therefore

[itex]

|\Omega-1|

[/itex]

is driven towards zero rather than away from it.

Doesn't inflation increase the volume of the universe, and hence wouldn't the density decrease rather than increase? Or am I misunderstanding the density parameter here?

The quantity 1/Ha is the comoving Hubble length, and determines which two regions can communicate now. The particle horizon on the other hand, separates two regions that could never have communicated. The horizon problem is solved by the possibility of greatly reducing the comoving Hubble length. Hence, regions that cannot communicate today were in causal contact early.

The way I understand this is that, the comoving Hubble length gets smaller with time. Therefore region that were within the comoving Hubble length earlier and hence could communicate and affect each other, are now out of contact. So even though we look at space and see regions that can't communicate now, there was a time when they could do so.

Does what I have just said make sense?

Finally my question on this part is, how does the particle horizon bit come into the picture? Can someone try and explain?

__Flatness Problem____Explanation I have__d/dt(1/Ha)<0

and therefore

[itex]

|\Omega-1|

[/itex]

is driven towards zero rather than away from it.

__My Confusion__Doesn't inflation increase the volume of the universe, and hence wouldn't the density decrease rather than increase? Or am I misunderstanding the density parameter here?

__Horizon Problem____Explanation I have__The quantity 1/Ha is the comoving Hubble length, and determines which two regions can communicate now. The particle horizon on the other hand, separates two regions that could never have communicated. The horizon problem is solved by the possibility of greatly reducing the comoving Hubble length. Hence, regions that cannot communicate today were in causal contact early.

__My Understanding__The way I understand this is that, the comoving Hubble length gets smaller with time. Therefore region that were within the comoving Hubble length earlier and hence could communicate and affect each other, are now out of contact. So even though we look at space and see regions that can't communicate now, there was a time when they could do so.

Does what I have just said make sense?

__My Confusion__Finally my question on this part is, how does the particle horizon bit come into the picture? Can someone try and explain?