I want to know if I power my Arduino mega with less than 5v, what will be the internal reference value that Arduin take to compare my analog input. Which is say 0-5v.
The default analog reference is Vcc so if Vcc is less (or greater) than 5V so will the analog reference.
There is also an optional internal 1.1V reference which is very stable (but there is a tolerance so it may not be exactly 1.1V).
If you are have a pot some other voltage-divider/proportional type of circuit it's better to have the reference tied to Vcc. If you need to measure absolute voltage accurately then of course, you need a stable reference.
The reference also mentions a 2.56V analog reference for the Mega.
INTERNAL2V56: a built-in 2.56V reference (Arduino Mega only)
I want to know if I power my Arduino mega with less than 5v
How much less? There’s a limit to how much you can reduce power supply and still run the clock at 16MHz.
4.5V is the lower limit for the Atmega2560.
There is an Atmega2560V that can run at lower voltages, but it is not used on Mega2560 boards.