As I have been there and done that myself, I KNOW EXACTLY how you feel, with the exception being that mine actually did cheat. Here's what I would ask you, though. Is he giving you any other indication at all to not trust him? Is anything else happening with him that is giving you this fear, or is it just the phone? Because if it's just the phone, I say be forthright and express your fears to him (really open up), and then let it go. Being 8 weeks pregnant is a bundle of emotions as it is, without adding this on top of it.
If nothing else is going on with him, I think the best thing you can do for both of you right now is to try to let go of that fear - for both your sakes. I know what that can do to a relationship, how the fear of something happening can overpower and undermine everything good about what's between the 2 of you.
If this is his first kiddo, or the first time dealing with a baby in the house, he's probably scared stupid right now (but won't ever admit that to you). I say try and find some quiet time between the 2 of you to just be by yourselves - if it's a dinner out, or just sitting on the front porch after your son has gone down and talk about your days. If you keep that connection alive with him, you'll be able to come through this a lot easier.
I wish you luck, girl, and my heart goes out to you. If it's any consolation, just know that someone else knows it feels like to be where you are, and has come out the other side of it with a stronger and more secure relationship.