Oh dear...I can see myself about a year ago here! Before I start, don't judge me...we have worked through it now!!!
I met DP online and we met up with the intention of just s"scratching an itch" if you see what I mean but we clicked and continued seeing each other, but I didn't really know where I stood so I continued to see someone else, on a purely physical basis! DP found out and was not happy which shocked me into realising hwat I could have lost and I soon snapped out of it. After that he checked my phone everyday...he doesnt know I know, but my phone works in such a way that when you open the menu it takes you to exactly where you were the last time you used it!! So i could always tell when he had checked my phone. It only served to really pee me off!!!
But then I noticed he was getting lots of texts at random times, that he still had his ex's number on his phone and that he would never let me look at his phone...all very suspicious, then I caught a glimpse of a text he received, a picture of a woman naked, needless to say i wasn't impressed as it looked a little like his ex...but he said it was his mates mucking around and it was "some random bird off the internet". But the seed of doubt was planted...everytime he went out I thought he was going to meet his ex, if he was half hour late from work etc.
I would recommend talking to him but I know that didn't work for us. We just continued, both knowing we loved each other, and now I trust him whole heartedly and he will even let me touch his phone, I have to ask though!!!
Before you snoop...if he has been honest with you about who he was texting...and he could have lied...he would probably be honest about anything going on. Imagine how hurt he would be if he found out you'd be snooping and he was innocent.
Not very helpful I know...but I think everyone is different, some people can talk through this kind of thing whereas we have to muddle through as talking doesnt seem to work!!