The words of Obi Wan in ROTJ might give us a hint
"To protect you both from the Emperor, you were hidden from your father when you were born. The Emperor knew, as I did,
if Anakin were to have any offspring, they would be a threat to him."
To me this means that both Vader and the Emperor are unaware of Padme giving birth, if not the whole thing doesnt make sence cause the emperor would turn the galaxy upside down to find them.