Considering that it's a veritable law of the universe that entropy increases over time, it appears to me that a low-entropy beginning of the cosmos is not only not improbable, but is in fact inescapable.
The low-entropy beginning of our cosmos does appear to be very highly improbable...Considering that it's a veritable law of the universe that entropy increases over time, it appears to me that a low-entropy beginning of the cosmos is not only not improbable, but is in fact inescapable.
But Carroll's point is that the physical state of the far-distant past is likely to have been similar to what the physical state of the far-distant future is likely to be: that is, a state of high entropy (that is, very disordered)! The quantum vacuum is just such a state.
The problem he's addressing is this: how do we get a low-entropy beginning for a cosmos? His tentative answer: as a negative pressure fluctuation of the high-entropy quantum vacuum. (He's not the only person to have suggested this, of course.)