A lot of people quote 10^ 500 as the number of different ways of compactifying the extra dimension in string theory. But I recall somoene saying at a talk that its now much larger than that. What's the current estimate?
Turok commented on this here:
“It would conclusively refute the ekpyrotic and cyclic models we proposed a decade ago. However, more recent bouncing universe models based on the Higgs field might still be viable.”
As a historical note, inflation was not designed to solve the horizon problem at all.. You can read Alan Guths account of how inflation was developed in his book
“The Inflationary Universe”. He is very clear inflation was developed for one reason alone, to solve the monopole problem.