What evidence can you find to explain Leontes' jealousy in Act 1 of The Winter's Tale?

This is a very interesting question, especially because the
eruption of Leontes' jealousy happens so fast. However, Shakespeare’s gives us some evidence that
justifies Leontes’ abrupt and uncontrolled feelings.

In act 1.2, we
learn that Polixenes, having been stayed long enough at Sicilia, wishes to return to Bohemia.
Leontes, in vain, tries to persuade him to stay one week longer, and then, he asks Hermione to
convince his friend, instead:

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Hermione “I had thought, sir, to have held my peace
until

You had drawn oaths from him not to stay. You,
sir,

Charge him too coldly. Tell him you are
sure

All in Bohemia’s well…” (1.2
28-32).

Nonetheless, the lines
exchanged between Hermione, and Polixenes become more and more ambiguous making us to ponder
about an eventual flirt between Leontes’ wife and the King of
Bohemia:

Hermione
“…Force me to keep you as a prisoner,

Not like a guest: so you shall
pay your fees

When you depart, and save your thanks. How say
you?

My prisoner? or my guest?...” (1.2
51-54).

Thus, when finally Polixenes
agrees to extend his stay in Sicilia, this decision is enough to produce in Leontes an intense
suspicion about his wife’s fidelity.

According to some scholars, in
spite of being apparently irrational, Leontes' jealousy is substantiated by the kind of
Patriarchal society existent in Jacobean England. Then, men were undoubtedly heads of families,
but, at the same time they were dependent on women’s reproductive capacities to produce
legitimate heirs. We see that in the play Hermione is nine months pregnant. and that Polixene has
been stayed in Sicilia for “nine changes of the wat’ry star”. This fact is enough to raise deep
suspicions in Leontes.

Lastly, we have to consider the nature of
Leontes and Polixenes’ friendship. As children they had been close friends, but the loss of
innocence had caused a change in this friendship- now, both men are married and have children.
Then, in adulthood, competitiveness might have tarnished their
friendship.