Trust

I recently saw a strange message on my husband's phone when I came out of the bathroom. I confronted him and he said he didn't know who it was from. Initially he didn't want to give me his phone as he wanted to prove to me this person was not in his contacts. We agreed that next time I ask him for his phone he would give it to me without hesitation. I am not the jealous snooping wife but I explained to him that I found his reluctance to give me his phone more concerning than the message. Today I asked him for his phone and he wouldn't give it to me. While hoovering I saw a message from someone called Amy pop up saying how positive and encouraging he is. I don't know who this person is and have no issues with him texting female friends but again  concerned about why he won't let me see his phone. I would have no issue giving him mine as I believe in transparency. I don't ever want to be the woman who checks her husband's phone but does anyone else think his behaviour is strange. We have been married for 4 years and it's the first time I've been in this type of situation. Just so you know I  am quite independent and once encouraged him to go travelling with two girls for three weeks as I was studying and couldn't go. I always support his boys night outs and encourage his hobbies/ friendships so am not the insecure type who wants him home all the time. I don't think he has or would cheat on me but I don't know what to do in this situation so would really appreciate some advice.