‘actual’ in ‘the actual world’ is an indexical term (like ‘here’ or ‘now’), not an indicator of a special ontological status.

 To know what a claim of transworld identity amounts to, and whether such claims are acceptable, we need to know what a possible world is, and what it is for an individual to exist in one.

Among those who take possible worlds seriously (that is, those who think that there are possible worlds, on some appropriate interpretation of the notion), there is a variety of conceptions of their nature. On one account, that of David Lewis, a non-actual possible world is something like another universe, isolated in space and time from our own, but containing objects that are just as real as the entities of our world; including its own real concrete objects such as people, tables, cows, trees, and rivers (but also, perhaps, real concrete unicorns, hobbits, and centaurs). According to Lewis, there is no objective difference in status between what we call ‘the actual world’ and what we call ‘merely possible worlds’. 

We call our world ‘actual’ simply because we are in it; the inhabitants of another world may, with equal right, call their world ‘actual’. In other words, according to Lewis, ‘actual’ in ‘the actual world’ is an indexical term (like ‘here’ or ‘now’), not an indicator of a special ontological status (Lewis 1973, 84–91; Lewis 1986, Ch. 1).