I would like to know what is the difference between Sleep mode and Deep sleep mode in android phone and what will be the impact of when phone goes to sleep mode and deep sle
Deep sleep mode doesn't have anything to do with hibernate and boot time, as somebody wrote in deleted answer.
You should not avoid the phone sleep, this will drain your battery very fast. To receive messages from server, you should use [C2DM] GCM which has the same basic characteristics as old fashion deprecated C2DM.
More info about the android sleep here: http://developer.android.com/reference/android/os/PowerManager.html