reading cookie on different domain

Our intranet site is something like http://intranet.company.com and an asp.net application runs when user goes to this address. The application reads a cookie and in its absense the app redirects to the login.aspx page. Upon successful login, the app creates a cookie storing the user info. This part has been running for quite some time.

Now the network admin created an 'alias' to this site that you can go to it just by typing 'http://intranet'. The app works fine here as well. The issue is since both these sites are technically the same, I want them to be able read the cookie created by the other.

In other words, if a user logs into to http://intranet and then opens a link like http://intranet.company.com/app1, the latter should recognize that a cookie has been created at 'http://intranet' and read the cookie and open app1 instead of redirecting to the login page.

I hope I've been clear enough.
Thanks
Arun