Could he be cheating?

I have been with my partner for 6 years, we've had some ups and downs like in any relationship but lately it feels like the relationship is one sided and it feels as though I'm putting in the effort and getting nothing back. I can just feel a strained atmosphere between us... (we have been going through a very bad time the last few weeks so could be that). But there's no affection there anymore, no sex, nothing. We don't even sleep in the same room.. He says it's because the baby keeps him awake and he needs rest for work. Fair enough but it's the same on weekends when he doesn't work. And I'm noticing the little things, like I could start a conversation about anything at all and he has no interest, he'll roll his eyes or just be blunt and not engage in the conversation, yet he can be on his phone and have plenty of time for that! There's no kiss goodnight anymore. He used to kiss me before going to work... That's stopped too. And twice now he's sat outside the house in his vehicle on his phone... Once was when he came home from work, he pulled up but didn't get out. Instead he sat there on his phone for ages. He did the same this morning leaving for work, he left the house but sat in his car for ages on his phone before pulling off. He has loads of time and patience for his phone but none for me. I just feel so unwanted by him. I've tried talking to him but he tells me to shut up and completely switches off, like he can't be bothered to talk about the state of the relationship. I've even asked him if he'd like me to just leave, and he tells me to stop being silly. It's like he doesn't want me but doesn't want me to leave either. It just feels like I'm fighting for a relationship where I'm the only one that actually wants it to work!