How to go about looking through his phone

Hi f25 here. So I recently moved in with my bf m29. We have been living together for a little over a month now. Since moving in together things seem to have drastically slowed down. He isn’t as lovey dovey anymore and the sex has slowed down even more. We were intimate like twice a day then I moved in and now it’s like every 4 days. I’m lowkey kinda concerned he might be cheating. He takes my car to work and he left for work rather early the other day. He is a friendly guy and im sure he’s friendly with females I’m just concerned with how friendly. Hes always been very open and honest with me but I know people can lie. Sometimes I see him get a Snapchat from females and he doesn’t seem to open it in front of me. I kinda have a feeling i should look through his phone but i dont know how to go about it. I feel kinda wrong looking through it while he sleeps. I used to do that with ex’s and i just feel like im too old for that. Should I just ask him to look through it? And what if i don’t find anything and he hates me for it. How should i go about it?