Alan Guth explains how eternal cosmic inflation explains the multiverse. Guth says that there is a lot of evidence for inflation. Also, the multiverse would explain the low number for the energy density of vaccuum.
Leonard Susskind explains that string theory proposes that there are 10^500 kinds of universes. Not just 10^500 universes but 10^500 possible kinds of universes.
Inflation results from repulsive gravity existing in the early universe.