S.C.
Hmm..sounds a little shady to me. If he was just carrying it around all the time, I wouldn't be too worried. I carry my phone around with me all the time. Maybe he puts it on vibrate so the ringing doesn't bother the family? Or maybe he genuinely doesn't want to miss a call. I think you need to talk to him about it. Ask him why he carries it around with him all the time. If you don't get a straight answer, then it's time to re-think things. I know a lot of people will tell you that going through his phone is a violation of his privacy, I disagree. If he has nothing to hide, then he won't care if you look at it.
I carry my phone with me everywhere. I have an app on my phone that lets me read books and I can often be found reading on my phone. It makes my husband crazy. He always thought I was texting until I told him what I was doing. It might be something as simple as that.
At any rate, it's time you talked to him about it.