Google frequently holds experimental field trials to test out new search features and then adds or discards them depending upon user response. The latest one is about finding your stuff faster. The field trial that’s on right now introduces you to searching your Gmail using Google.com instead of digging through the mountain of emails in your inbox.
You may have already tried out the enhanced flight tracking features that help you search for upcoming flights using the [my flights] query on Google.com. Similarly, you can now use and search with [my purchases] to see a list of recent online purchases from select merchants like Amazon and track their arrival. Planned a holiday? Check the hotel bookings with [my hotel reservation] or [my restaurant reservations] if you booked through OpenTable. Events like concerts, sports games etc. are also covered with a query like [my events] to easily retrieve information from Ticketmaster or Eventbrite.
Google calls for users to join the field trials for a better search experience no matter which device you are using. These parameters are also available on mobile devices where SSL is on by default. Also note the notification on the Field Trial page which says “This trial is only accessible on google.com in the U.S. in English for @gmail.com addresses (not available on Google Apps accounts)”.