How to know if someone is a Deva or an incarnation of a Deva?
Do Hindu scriptures talk about how to determine whether someone who claims he is a god or avatar of a god, is actually one?
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I first want to differentiate between avatara of Bhagavan, and a temporary appearance of a Deva, because the word 'God' is used loosely in your question.
Devas are Svarga-loka vasis (residents). They may appear briefly on earth for a specific purpose, whether selfish or altruistic. An example is during Nala-Damayanti Swayamvar in Mahabharata Nalopakhyana parva, when 4 devas disguised themselves as Nala.
And when, O Bharata, the names of the monarchs were proclaimed, the daughter of Bhima saw five persons all alike in appearance. And beholding them seated there, without difference of any kind in form, doubt filled her mind, and she could not ascertain which of them was king Nala. And at whomsoever (among them) she looked, she regarded him to be the king of the Nishadhas. And filled with anxiety, the beauteous one thought within herself, 'Oh, how shall I distinguish the celestials, and how discern the royal Nala?' And thinking thus, the daughter of Vidarbha became filled with grief. And, O Bharata, recollecting the marks belonging to the celestials, of which she had heard, she thought, 'Those attributes of the celestials, of which I have heard from the aged, do not pertain to any of these deities present here upon the earth.' And revolving the matter long in her mind, and reflecting upon it repeatedly, she decided upon seeking the protection of the gods themselves.
Damayanti could not distinguish them to find out her true 'human' Nala, so she asked the Devas for differentiating characteristics.
And thereupon she beheld the celestials unmoistened with perspiration, with winkless eyes, and unfading garlands, unstained with dust, and staying without touching the ground. And Naishadha stood revealed to his shadow, his fading garlands, himself stained with dust and sweat, resting on the ground with winking eyes
- do not sweat
- do not blink
- do not cast shadow
- garlands do not fade
- are not defiled by dust
- feet do not touch ground.
For Manushyas, all of above happens. So that's difference between deva and manushya.
Now, for avatara of Bhagavan (Paramatma Vishnu) himself, there are other distinguishing characteristics - His feet have auspicious marks of shanka & chakra, He wields Sudarshana & Panchajanya, many more, depending on type of avatara.