Is Infinity Possible

"Infinity" has many interpretations according to context. There is a difference, for example, between the possibility of infinity as 'picturable' and its possibility as 'mathematically functional'. And with respect to the later, different geometries used by science deal with 'infinity' in different ways. So when you ask for 'the science of infinity' there is no single answer.
Just to underscore the point, the celebrated mathematicion involved with infinity, Georg Cantor, showed that there were 'different sized infinities', but to blow the mind even further, Cohen got the Field's medal for proving that there both 'was' and 'was not' an infinity of size between Cantor's discoveries !
Aren't you glad you asked ?

Everything is Infinite.
Or it wouln't 'be' (exist)