Using local storage for all subdomains

I have 2 subdomains and 1 main page: product, expert.product and user.product. After user login in the main page: product.com, my code will check which role of user belongs to: expert, user. If user’s role is expert, it will direct user to expert.product.com. I would like to use a local storage for all subdomains as Google. When user sign in Google, user can access subdomains of google: mail or hangouts without re-signing when user goes to mail or hangouts. Could anyone help me for this case? Many thanks in advanced.