I can't understand the condition for inflation that Liddle presents in his book,(adsbygoogle = window.adsbygoogle || []).push({});

Cosmological Inflation and Large-Scale Structure A.Liddle, Pg 51:

[tex]

\frac{d}{dt} \frac{H^{-1}}{a} <0

[/tex]

Because [itex]\frac{H^{-1}}{a}[/itex] is the comoving Hubble length, the condition for inflation is that the comoving Hubble length, which is the most important characteristic scale of the expanding Universe, is decreasing with time. Viewed in coordinates fixed with the expansion, the observable Universe actually becomes smaller during inflation because the characteristic scale occupies a smaller and smaller coordinate size as inflation proceeds.

Shouldn't be the opposite? The the observable shouldn't became bigger instead of smaller? I know that this relation cames from the other one which states that during the inflation the scale factor is accelerating but the I am not getting the physical picture.

Thanks

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# Condition for inflation presented by Liddle

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