Well you've opened Pandoras box .. you will never be able to forget it and put it behind you until you know the truth .. if you sit on it and don't say anything it will eat away at you and your relationship until there is nothing left fact, which means you will have to see yourself without him. 

Your only way out of this is to admit to him you have been concerned due to the fact that people have been asking so you decided to have a look and saw he had deleted her messages and what was up , if you both trust and love each other as much as you say you do... looking him dead in the eyes should give you a decent idea if he's lying. 

Either way the trust has now been damaged on both sides and if he's innocent you will just have to apologize and work for it back.