Is it permissible to supplicate to Allah with “Ya Allah” or “Ya Rabb,” based on one researcher’s opinion that the vocative particle “Ya” is used by a superior addressing an inferior, and that all supplications in the Holy Qur’an do not begin with it when addressing Allah?

There is no objection to using the vocative particle "ya" in supplication. This has been reported in numerous hadiths and narrations from the Prophet (peace be upon him), the Companions, and the Salaf. Examples include the Prophet's saying to Aisha: "Ya Dhal Jalali wal Ikram (O, Lord of Majesty and Honor)," and his saying to Anas: "Ya Hayyu Ya Qayyum (O, The Ever-Living, The Self-Subsisting)." Some of the Salaf interpreted the Greatest Name of Allah as "Ya Dhal Jalali wal Ikram."

As for the Quran's preference for omitting "ya" when the prophets supplicated with the word "Rabb (Lord)" in most instances, this does not indicate prohibition. Rather, it is to emphasize the proximity of the invoked "Rabb," and because the word "Rabb" is more frequently used in supplication, it was simplified for ease of pronunciation. The omission in the Quran was not limited to the word "Rabb" but appeared in other places to lend grandeur to the expression.