How do Anakin and Padme keep their marriage a secret?

But here's the thing; Anakin and Padmé had the advantage of a galaxy-wide war going on, so everyone was too busy either fighting in the war, working hard at their jobs, or were distracted by the war's effects on everyday life. Nobody really had the time to investigate one jedi and one senator in the midst of all that.

Only people really close to them ever found out about the relationship, or were in on the secret. In fact, Obi-Wan was aware that Anakin had feelings for Padmé for years, but he didn't know just how far the two of them had gone until he came to Padmé's apartment that one day, asking for help in finding him, and she was too distracted at the time to hide her baby bump properly.

My theory is that everyone on Coruscant knows they're boinking, they just don't know they're married! The ceremony was totally private, and a long way from the senate.

Remember, we're never told that Jedi are celibate, just that theyre not supposed to get seriously attached. That leaves a bit of room for relieving the hormones, maybe people turn a blind eye to a bit of fun along as things don't get too serious.

They do it up the yazoo.