I have just started my PhD with the same advisor of my Master Degree. We are working in Cosmology, a new topic for my advisor who has worked for years in QFT. I owe him a lot and I learnt a lot of things from him, but now I am facing a really big problem: he is not an expert in Cosmology. He pushed me to work on ideas which I realized to be meaningless. Furthermore, I feel like we are working to publish, not to learn something. I suggested to work with a Professor of another university, a friend of my supervisor, who is a really famous master of the subject, but he didn't agree.
I don't know what to do. I really feel bad, because I don't want to waste my PhD but I don't want to argue with my advisor. What can I do?