I'm working on an android application that supports push notification through GCM. I want to know is it possible to send the push notification message that has been receieved on your smartphone or table and display it on your TV via Chromecast?
Basically...no.
Chromecast allows you to put a web page on your TV and then allows your device to communicate with that web page. That's it.
You could open a Chromecast app when you receive a push notification...or notify a Chromecast receiver app that's already running, but there's no way to influence what comes up on the screen when you're not running an app.