What is the story of Viṣṇu taking the form of Vāmana(dwarf)?

 

Rig Veda mentions the same formless ENERGY or BRAHMAN with various epithets, viz., AGNI, INDRA, Viṣṇu, SARASWATI, VARUNA, etc.

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a) Viṣṇu was mentioned as the Formless ENERGY/Brahman in Rig Veda 2.1.3.

त्वमग्न इन्द्रो वृषभः सतामसि त्वं विष्णुरुरुगायो नमस्यः । त्वं ब्रह्मा रयिविद्ब्रह्मणस्पते त्वं विधर्तः सचसे पुरंध्या ॥
tvam agna indro vṛṣabhaḥ satām asi tvaṃ viṣṇur urugāyo namasyaḥ | tvam brahmā rayivid brahmaṇas pate tvaṃ vidhartaḥ sacase puraṃdhyā ||

English translation:

You, Agni, as bull of beings, are Indra; you, wide-going, worthy of homage, are Viṣṇu. You, o lord of the sacred formulation, finder of wealth, are the Brahman; you, o Apportioner, are accompanied by Plenitude.

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b) Viṣṇu taking 3 steps was mentioned in Rig Veda 1.154.3, covering Earth, mid-space and Heaven.

The steps in Earth, mid-space and Heaven indicates in esoteric/spiritual sense the Brahman pervading in the entire spiritual realm of the individual.

प्र विष्णवे शूषमेतु मन्म गिरिक्षित उरुगायाय वृष्णे । य इदं दीर्घं प्रयतं सधस्थमेको विममे त्रिभिरित्पदेभिः ॥
pra viṣṇave śūṣam etu manma girikṣita urugāyāya vṛṣṇe | ya idaṃ dīrgham prayataṃ sadhastham eko vimame tribhir it padebhiḥ ||

English translation:

Let my fortifying thought go forth to Viṣṇu, the mountain-dwelling, wide-ranging bull, who alone with just three steps measured out this dwelling place here, long and extended,

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c) Vishnu covering Earth, space, and heaven as Vāmana (dwarf) and pushing Bali into nether world was not mentioned in the Rig Veda.

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d) Vishnu as Vāmana (dwarf) - vāmano ha viṣṇurāsa", was first mentioned in Shatapatha Brahmana 1.2.5.5.

1:2:5:1 The gods and the Asuras, both of them sprung from Pragâpati, were contending for superiority. Then the gods were worsted, and the Asuras thought: 'To us alone assuredly belongs this world!

1:2:5:2. They thereupon said: 'Well then, let us divide this world between us; and having divided it, let us subsist thereon!' They accordingly set about dividing it with ox-hides from west to east.

1:2:5:3. The gods then heard of this, and said: 'The Asuras are actually dividing this earth: come, let us go to where the Asuras are dividing it. For what would become of us, if we were to get no share in it?' Placing Vishnu, (in the shape of) this very sacrifice, at their head, they went (to the Asuras).

1:2:5:4. They then said: 'Let us share in this earth along with yourselves! Let a part of it be ours!' The Asuras replied rather grudgingly: 'As much as this Vishnu lies upon, and no more, we give you!'

1:2:5:5. Now, Vishnu was a dwarf.

1:2:5:7. Having thus enclosed him on all (three) sides, and having placed Agni (the fire) on the east side, they went on worshipping and toiling with it (or him, i.e. Vishnu, the sacrifice). By it they obtained (sam-vid) this entire earth; and because they obtained by it this entire (earth), therefore it (the sacrificial ground) is called vedi (the altar). For this reason they say, 'As great as the altar is, so great is the earth;' for by it (the altar) they obtained this entire (earth). And, verily, he who so understands this, wrests likewise this entire (earth) from his rivals, excludes his rivals from sharing in it.

 

The text explicitly establishes Vishnu as a dwarf (Vāmana) and records the gods winning back only the Earth from the Asuras by measuring out a space equal to Vishnu’s body.

The narrative focuses entirely on the Asuras agreeing to give the Devas as much land as Vishnu can lie upon. The Devas enclose Vishnu on the ground, and by doing so, they obtain and step across this entire Earth.

It is to be noted that mid-space (antarikṣa) and heaven (dyu) are not part of the stride narrative in Shatapatha Brahmana 1.2.5. The story here operates on the size of a sacrificial altar (vedi) on Earth rather than a cosmic expansion across the three worlds.

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It was only later, in texts like the Bhagavata Purana, that authors combined the dwarf persona from the Brahmanas with the three cosmic steps from the Rigveda to create the famous Trivikrama legend (encompassing Earth, space, and heaven to defeat King Bali).