It's often said that inflation doesn't solve the arrow of time problem,
that the initial state at the time of the big bang in unnatural. But I can
make an argument that Eternal inflation does solve the AOT problem by
mandating a very low total entropy at the moment of the Big Bang. There must be
something wrong with argument, as far as I know no one else is making it. So
it would be great if someone took a go at this.
The argument goes like this. Given the launch of inflation we know it must
be eternal if the mean decay time
for vacuum energy is greater than the efold time. It's difficult to come
up with inflation models that evade this condition. An inflating space time
has no AOT, assuming an equation of state of -1 , , which is approximately
correct in all inflation scenarios, the De Sitter Horizon is constant, or
near constant.
What we call the Big Bang is the decay of the inflaton field creating a
region of space time with an equation of state of +1/3 ( except for any
residual vacuum energy) causing a rapid expansion of the horizon. This rapidly
drops the entropy density making room for entropy production. In addition,
the inflaton field decay generates all the fundamental particles allowing
the well established evolution scenarios we have of the early Universe to
create the Universe we observe today. This ties the expansion of the
Horizon to the cosmic AOT. Even today the mean entropy density continues to fall
, local entropy density is far below the Bekenstein limit. Why doesn't
this explain the cosmic AOT?