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Chaos is defined as an aperiodic long-termed behavior, that is very sensitive to initial conditions.

Now from this definition I can only conclude that the adjective 'chaos' is a mere analogy, since there is nothing aperiodic (or periodic) during inflation. The inflaton follows a nice, smooth (often taken to be a quadratic) potential.

Furthermore the initial conditions are essentially that $$\ddot{\phi}\approx 0 \quad \text{and}\quad \dot{\phi}\text{ is small},$$ shows that these are not very stringent wrt to the final result: at whatever 'speed' you begin, as long as it small enough it is ok....

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  • $\begingroup$ I believe it is the massive quantum fluctuations which give this rather misleading name to a property of spacetime in regions with no reasonable analytical manifold. $\endgroup$ – GRrocks May 29 '14 at 14:51
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Linde's model, unlike the first model proposed by Guth, assumes random initial conditions. So

Chaotic = almost arbitrary initial conditions

This implies that not all regions of space will undergo inflation. However the patches that do no inflate will become insignificant, while the other will dominate due to the exponential increase in volume.

In fact this quote of Linde is quite helpful:

[Chaotic inflation] creates order out of chaos, not by destroying previous chaos, but by exploding those parts that are capable of becoming non-chaotic.

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For what i remember a chaotic inflation potential would be of the form $$\sim\lambda\varphi^4$$ and when $\lambda<<1$ you essentially have a flat potential where no points seems to be favorite as starting point for slow roll.

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