You can use contexts. Add your user object to childContextTypes in your root App Component. Now you can get this object on any component down the tree.
Without contexts, you have to pass down the user object as props to every component which requires it, which is not an elegant solution. Another solution is to get the user object from flux store, if you use any.
You can learn more about contexts here.
Note: Context is an experimental feature. It's API may change in future.