Going through boyfriends phone

Alexis
So quick question ladies, please don't judge me! 
My boyfriend used to be a big "ladies man" and talk to and have sex with a lot of women, we were best friends before we started dating so I feel like I KNOW him. He's changed ALOT of things for me and settled down. No, I don't think he's cheating BUT I'm always wondering if he still texts those old girls from the past. He's a heavy sleeper so there's always the chance to check just in case... What do yall think I should do?...