When a human egg cell is fertilised to form a zygote is it possible
for the zygote to be divided into two separate embryos by an
unpredictable quantum event such as a cosmic ray resulting in the
formation of identical twins?

"unpredictable"? By definition, quantum events are always only
predictable statistically so they are all unpredictable in any
real-world sense.

A cosmic ray is not necessary to trigger such an event.

Some twins are almost certainly created by quantum events which may be
entirely internal or may be triggered by external forces such as a
cosmit ray, although many more are probably caused by some biochemical
reaction operating far above the quantum level.

Monozygotic twins occur

Whether that is down to a cosmic ray or food additives, is a moot point.