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The most commonly cited candidate for the homeland of the Proto-Indian-Iranian culture is the Andronovo Archaeological Complex, while others place their origin within the Indus Valley Civilization<ref name="The Aryan-Non Invasionist Model">The Aryan Non-Invasionist Model by Koenraad Elst</ref>. Historical linguists broadly estimate that a continuum of Indo-Iranian languages probably began to diverge by 2000 BCE, if not earlier,<ref>Mallory, J.P. (1989). In Search of the Indo-Europeans: Language, Archaeology and Myth. London: Thames & Hudson, 38–39. ISBN 0-500-27616-1.</ref> preceding both the Vedic and Iranian cultures. The earliest recorded forms of these languages, Vedic Sanskrit and Gathic Avestan, are remarkably similar, descended from the common Proto-Indo-Iranian language. The origin and earliest relationship between the Nuristani languages and that of the Iranian and Indic groups is unrecoverably obscure.
There are multiple hypotheses as to the expansion of the Indo-Iranians. One such hypothesis suggests that the Indo-Iranians expanded widely into Central Asia from the Ural River in the west to the Tian Shan in the east, taking over the area occupied by the earlier Afanasevo culture, and defined by Transoxiana and the Hindu Kush (mountains) in the south. This region would later become for the most part exclusively Iranian.
 Two Wave Theories
Asko Parpola and other scholars have proposed a two wave (or multiple wave) model for the migration of Iranians and Indo-Aryans.
 First wave
Based on linguistic evidence scholars argue that the Indo-Iranians were the first to exploit the chariot, leading what is sometimes called the first wave of Indo-Iranian expansion. It is assumed that this expansion went into the Caucasus, the Iranian plateau, Afghanistan, and, India. They also expanded into Mesopotamia and Syria, and introduced the horse and chariot culture to this part of the world.
They left linguistic remains in a Hittite horse-training manual written by one "Kikkuli the Mitannian". Other evidence is found in references to the names of Mitanni rulers and the gods they swore by in treaties; these remains are found in the archives of the Mitanni's neighbors. The time period for this is about 1500 BCE.<ref>Mallory, J. P., Mair, Victor H. (2000). The Tarim Mummies. London: Thames & Hudson, 257. ISBN 0-500-05101-1.</ref>
The standard model for the entry of the Indo-European languages into India is that this first wave went over the Hindu Kush, either into the headwaters of the Indus or the Ganges (and probably, both). The earliest stratum of Vedic Sanskrit, preserved only in the Rigveda, is assigned to roughly 1200 BCE.<ref>Mallory and Mair 2000:258</ref> From the Indus, the Indo-Aryan languages spread with the migrants who, from c. 1500 BCE to c. 500 BCE, were able to spread over the northern and central parts of the subcontinent, sparing the extreme south. The Indo-Aryans in these areas established several powerful kingdoms and principalities in the region, from eastern Afghanistan to the doorstep of Bengal. The most powerful of these kingdoms was Magadha, which lasted until the 4th century BCE, when it was conquered by Chandragupta Maurya and annexed into the Mauryan empire.
In eastern Afghanistan and southwestern Pakistan, whatever Indo-Aryan dialects that were spoken there were eventually pushed out by the Iranian languages. Most Indo-Aryan languages, however, were and still are prominent in the rest Indian subcontinent. Today, Indo-Aryan languages are spoken in India, Pakistan, Bangladesh, Nepal, Sri Lanka and the Maldives.
 Second wave
The Second Wave is interpreted as the Iranian wave.<ref>Mallory 1989:42–43</ref> The Iranians would take over all of Central Asia, Iran, and for a considerable period, dominate the European steppe (the modern Ukraine) and intrude north into Russia and west into central and western Europe well into historic times and as late as the Common Era. The first Iranians to reach the Black Sea may have been the Cimmerians in the 8th century BCE, although their linguistic affiliation is uncertain. They were followed by the Scythians, who are considered a western branch of the Central Asian Sakas. The Rigvedic Kambojas may correspond to the Nuristani branch of Indo-Iranian. The Medes, Parthians and Persians begin to appear on the Persian plateau from ca. 800 BCE, and the Achaemenids replaced Elamite rule from 559 BCE.
In Central Asia, the Turkic languages and culture have replaced Iranian, but a substantial minority remains in Uzbekistan and Turkmenistan. The Iranian languages are now confined to Iran, Kurdistan, Afghanistan, western Pakistan, Tajikistan, Turkey and the Caucasus.
 The Sogdiana model
Nichols (1997) has proposed a homeland to the east of the Caspian sea, in the vicinity of ancient Bactria-Sogdiana. <ref>Nichols, Johanna. 1997a. “The Epicentre of the Linguistic Spread.” In Roger Blench and Matthew Spriggs (eds.) Archaeology and Language I: 122-148. London: Routledge. --1997b. The Eurasian Spread Zone and the Indo-European Dispersal. In Roger Blench and Matthew Spriggs (eds.) Archaeology and Language, II. London: Routledge.</ref>
 Out of India model
The Out of India theory as suggested by Koenraad Elst holds that the Indo-Iranians were remnants of the Proto-Indo-European culture that resided within the Indian subcontinent in the 5th millennium BC<ref name="The Aryan-Non Invasionist Model">The Aryan Non-Invasionist Model by Koenraad Elst</ref>. After the split of the Proto-Indo-Iranians. The Iranians would have migrated towards the Hindu Kush and eventually towards Central Asia making their discovery of the chariot during this period.<ref name="The Aryan-Non Invasionist Model">The Aryan Non-Invasionist Model by Koenraad Elst</ref>
The Iranian expansion then continued throughout Central Asia and as far as Mesopotamia, forming a large Iranian empire. This concept is similar to the Second Wave of the Indo-Iranian migrations. Iranian languages became extinct in its eastern territories as a consequence of Turkic migration. During this period of the expansion to the west by the Iranians, the Indo-Aryans are suggested to have travelled eastwards through the Gangetic plains. They occupied much of North India through these movements away from the Indus Valley.<ref name="The Aryan-Non Invasionist Model">The Aryan Non-Invasionist Model by Koenraad Elst</ref>
Archaeological cultures associated with Indo-Iranian expansion include:
- Central Asia
- Poltavka culture (2700-2100 BCE)
- Andronovo horizon (2200-1000 BCE)
- Sintashta-Petrovka-Arkaim (2200-1600 BCE),
- Alakul (2100-1400 BCE)
- Fedorovo (1400-1200 BCE)
- Alekseyevka (1200-1000 BCE)
- Bactria-Margiana Archaeological Complex (2200-1700 BCE)
- Srubna culture (2000-1100 BCE)
- Abashevo culture (1700-1500 BCE)
- Yaz culture (1500-1100 BCE)
Parpola (1999) suggests the following identifications:
|date range||archaeological culture||identification suggested by Parpola|
|2800-2000 BCE||late Catacomb and Poltavka cultures||late PIE to Proto-Indo-Iranian|
|2000-1800 BCE||Srubna and Abashevo cultures||Proto-Iranian|
|1900-1700 BCE||BMAC||"Proto-Dasa" Indo-Aryans establishing themselves in the existing BMAC settlements, defeated by "Proto-Rigvedic" Indo-Aryans around 1700|
|1900-1400 BCE||Cemetery H||Indian Dasa|
|1800-1000 BCE||Alakul-Fedorovo||Indo-Aryan, including "Proto-Sauma-Aryan" practicing the Soma cult|
|1700-1400 BCE||early Swat culture||Proto-Rigvedic = Proto-Dardic|
|1700-1500 BCE||late BMAC||"Proto-Sauma-Dasa", assimilation of Proto-Dasa and Proto-Sauma-Aryan|
|1500-1000 BCE||Early West Iranian Grey Ware||Mitanni-Aryan (offshoot of "Proto-Sauma-Dasa")|
|1400-800 BCE||late Swat culture and Punjab, Painted Grey Ware||late Rigvedic|
|1400-1100 BCE||Yaz II-III, Seistan||Proto-Avestan|
|1100-1000 BCE||Gurgan Buff Ware, Late West Iranian Buff Ware||Proto-Persian, Proto-Median|
|1000-400 BCE||Iron Age cultures of Xinjang||Proto-Saka|
The Indo-European language spoken by the Indo-Iranians in the late 3rd millennium BC was a Satem language still not removed very far from the Proto-Indo-European language, and in turn only removed by a few centuries from the Vedic Sanskrit of the Rigveda. The main phonological change separating Proto-Indo-Iranian from Proto-Indo-European is the collapse of the ablauting vowels *e, *o, *a into a single vowel, Proto-Indo-Iranian *a (but see Brugmann's law). Grassmann's law and Bartholomae's law were also complete in Proto-Indo-Iranian.
 See also
- Jones-Bley, K.; Zdanovich, D. G. (eds.), Complex Societies of Central Eurasia from the 3rd to the 1st Millennium BC, 2 vols, JIES Monograph Series Nos. 45, 46, Washington D.C. (2002), ISBN 0-941694-83-6, ISBN 0-941694-86-0.
- J. P. Mallory & Douglas Q. Adams, "Indo-Iranian Languages", Encyclopedia of Indo-European Culture, Fitzroy Dearborn, 1997.
- Asko Parpola, 'The formation of the Aryan branch of Indo-European', in Blench and Spriggs (eds), Archaeology and Language III, London and New York (1999).
- Michael Witzel, "The Home of the Aryans", in: Anusantatyai. Fs. für Johanna Narten zum 70. Geburtstag, edd. Hintze, Tichy. (Münchener Studien zur Sprachwissenschaft, Beihefte NF 19) Dettelbach: J.H. Roell (2000), 283–338  (PDF).