Girlfriends ex boyfriend is a problem?

So my girlfriend and I have been dating a year now and at about into 8 months of our relationship we moved in together. She has this ex boyfriend who I didn't think was a problem until we started living together i found out the truth. He texts her a lot things like I miss u come hang out with me etc. It bothers me soo much. She says it's nothing but she has constantly talked about things him and her have done in the past (places and little things they did together). Well she has a diary which she left out one day and i shouldn't have read it but i was curious to see if maybe i was being played so i read a little bit of it. what i found was astounding! she said things like how her and him were so perfect and she never loved n e one like that she misses him...it really hurt me bc i thought we were starting to connect. I havent told her even yet that i read it but now she has seemed to grow colser to me and tells me these things. SHould I trust her? There have been no more diary entrys