Receive sms on android phone without GSM module
There are exactly two ways of sending an SMS. Both of which require more than "just" an Arduino.


Directly using GSM - for which you NEED a GSM shield
Indirectly using an Internet Gateway - for which you NEED some form of internet connection.


Since you have an aversion to 1, 2 is your only option. So you require some extra hardware (unless you have an Arduino with built in WiFi or Ethernet) to connect your Arduino to the internet. Then you have to pay an SMS gateway provider to allow you to send SMS messages through them, and implement their API in the Arduino.  

Also you need an internet connection available wherever the Arduino happens to be.

All in all a lot of work and you're really no better off than using a GSM shield.