##### What's Hot

When the slow-roll parameter $\epsilon_H$ is smaller than $H^2/M_{\rm Pl}^2$,
the quantum fluctuations of the inflaton after the horizon crossing are large
enough to realize eternal inflation. Whereas they do not generate a sufficient
amount of density fluctuation of the inflaton to produce the black hole in
quasi-de Sitter space, they can also generate the sizeable density fluctuation
of the radiation when the number of degrees of freedom increases rapidly in
time, as predicted by the distance conjecture. We argue that the condition that
the density fluctuation of the radiation is not large enough to produce the
black hole until the end of inflation is equivalent to the no eternal inflation
condition. When the radiation emitted by the horizon does not produce the black
hole, even if the number of degrees of freedom increases in time, the
information paradox does not arise for $\epsilon_H$ larger than $10^{-7} (H^2/ M_{\rm Pl}^2)$ and time scale shorter than $10^4 (M_{\rm Pl}/H^2)$. Regardless
of the presence of the information paradox, a static observer cannot retrieve a
sufficient amount of information, which is consistent with the complementarity.

Share.