What has God to do with "Porphyria's Lover"? What is the meaning of the last line, "And yet God has not said a word!"
This is an excellent and intriguing question! Well done for asking it! It is important to realise that Browning in this poem creates an unreliable narrator whose words we clearly come to doubt as the poem progresses. Note how he convinces himself that Porphyria did not suffer when he killed her, though we, his audience, are far from certain:
No pain felt she;
I am quite sure she felt no pain.
The repetition seems to underlie the sense of doubt that we have in the narrator's account. As the poem ends, he seems to be looking for some kind of ultimate justification that he has done the right thing in killing her and thus possessing her forever:
Porphyria's love: she guess'd not how
Her darling one wish would be heard.
And thus we sit together now,
And all night long we have not stirr'd,
And yet God has not said a word!
In the same way that the narrator convinces himself that Porphyria felt no pain as he strangled her, so he creates a justification for what he has done. The silence of God is seen as an approving silence at the end of the poem, one that condones the "pure" actions of the narrator in immortalising and cementing their love.