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Why does comoving Hubble radius increase with time? 
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#1
Feb2712, 04:35 AM

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I am looking at inflation at the moment, and it says in my textbook that (aH)^(1) is constantly increasing in matter or radiation dominated epochs.
a is always positive and always increasing. This tells me that da/dt is positive. I think that setting the universe to MD/RD means that da/dt is decreasing with time (eg a decelerating universe as there is no cosmological constant driving expansion). So dt/da (which is another expression for comoving Hubble radius) is increasing with time. Have I got this right? 


#2
Feb2712, 07:11 AM

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da/dt decreasing in time is not a decelerating universe, it's a contracting one.
EDIT: This statement is obviously incorrect. See below for my efforts to redeem myself... 


#3
Feb2712, 08:38 AM

P: 61

If todays value of da/dt is lower than yesterdays, but they are both greater than 0, doesn't that mean the universe is expanding, but that the rate of expansion is slowing down?



#4
Feb2712, 08:43 AM

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Why does comoving Hubble radius increase with time?



#5
Feb2712, 02:15 PM

P: 59

Ummm...no one has answered the question correctly so far.
Comoving Coordinates (and Comoving distances) do NOT increase with the expansion of the Universe, and do not increase in time. That is the whole point of the Comoving coordinate system. Proper distances increase in time. The Hubble Paramater is measuring the rate of change of Scale Factor (da/dt) divided by the Scale factor (a). The Scale factor is timedependent, and is directly related to the Proper distance. 


#6
Feb2712, 02:23 PM

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It does not follow that all quantities measured in comoving coordinates are constant  what would be the point of using them then?? Any proper distance that is not increasing with the expansion will have nonconstant comoving coordinates. The Hubble radius, [itex]H^{1}[/itex], measured with respect to comoving coordinates is the comoving Hubble radius, [itex](Ha)^{1}[/itex]. It very much depends on time. 


#7
Feb2712, 02:31 PM

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#8
Feb2712, 02:36 PM

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#9
Feb2712, 02:44 PM

P: 59

And I agree, I have probably needlessly confused the question in the original post. 


#10
Feb2712, 03:12 PM

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#11
Feb2712, 04:57 PM

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#12
Feb2812, 02:21 AM

P: 61

Hooray! Nothing is simple in cosmology, is it? :D



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