How do I run cron as an authenticated user?
I don't think this is possible w/o some shenanigans.  If you look at drupal_cron_run(), you will see that it changes the user to anonymous (around line 5337 in includes/common.inc):

// Force the current user to anonymous to ensure consistent permissions on
// cron runs.
$original_user = $GLOBALS['user'];
$GLOBALS['user'] = drupal_anonymous_user();


The only way around this would be to implement a hook_cron() and alter its weight so that it gets called first, and have it swap in the user that you want (which can be a little tricky in some cases.  This may also cause problems with some cron hooks, like search_cron(), which assume the anonymous user, and end up with weird results (in this case, there may be a security problem where privileged information is revealed to the anonymous user).