The migration into India is historically accurate, that much is known. But this gets a little complex in India because of religion and politics, so let's try to clarify this.

This used to be written as an invasion into South Asia from the Central Asian steppes, which British imperialists then used to help justify their colonization of India--essentially they said "hey white people conquered this place in the past so we have justification for doing it again."

The implications of this are that India produced nothing original, that everything stemmed from others. So that's part of why some Indian nationalists have an issue with it. The other reason why some have a problem is due to the language factor: Sanskrit is looked at as a pure language in Hinduism--something sacred. If it is understood to be just a branch of Indo-European languages, then that means it is ultimately derived from another, more ancient tongue and hence not pure and therefore causes religious problems for Hindus.

However, these arguments still characterize the Indo-Europeans movement into South Asia as an invasion, which is totally wrong. This is because over the past...century or so we've uncovered more and more evidence that changes how we understand this event. The word invasion implies a group of people with a set identity who go out to explicitly invade and conquer an area for some reason. That's not what happened.

What is now known is that the Indo-Europeans migrated out in waves consisting of very small bands of warriors, not whole tribes or nations. Using comparative mythology and what ancient sources are available, what happens is not a conquest of a nation (like Germany taking over France or something), but rather a phenomenon known as Elite Transfer. Essentially the small warrior band conquers and replaces not the people, but just the top tier of the society.

The result was the import of some ideas and technology: horses, chariots, some religions elements, etc. But here's the thing that should be emphasized: the migration of bands of people into South Asia did happen, we know that. To say otherwise is to be blinded by modern politics and to ignore evidence. Taking these migrations into account, they should be looked at in the whole context of South Asian history for what it really is--a small amount of people brought some ideas into South Asia, and the end result was the eventual mixing of those concepts with native ones. Over the centuries and millennia some ideas from Persia and Greece and China are brought in. What this does is to stimulate the native people and inspire them to create one of the most absolutely beautiful, long lasting, and highly influential cultures and civilizations in world history.

I do not know if you're Indian, or just an inquirer. But if you are Indian I am very happy for you! You belong to a mighty culture that has impacted so much of the world by taking in other ideas and rejecting what isn't needed to create something uniquely their own. The religious concepts brought with the Indo-European Migrations leads to (once they blend with native stuff) the eventual creation of Hinduism and then Buddhism, two monumental faiths that have not only given birth to astounding amounts of philosophy and science, but to stunningly gorgeous art and architecture.

I hope I helped answer you question!

I'm no geneticist, but to the point of the second article: you don't need genetics to know that there was some movement of peoples from the Pontic steppe to South Asia. Sanskrit (and modern Indic languages) are all Indo-European. This is well-established fact, as well-established as the fact that night follows day, and there is no way to account for that without some migration to the Indian subcontinent.

By comparing potentially cognate words and finding sets of regular (i.e., exceptionless) correspondences, we can establish that a set of languages are related to each other. There are innumerable such correspondences clearly linking Indic languages to other Indo-European languages. To list a few:

1. PIE *a, *o, *e (both short and long) collapsed to Sanskrit a (keeping their length): PIE *kʷe 'and' comes out in Sanskrit as ca (n.b. non-Sanskritists: c is like the ch of English cheese), PIE *kʷos 'who, what' comes out in Sanskrit as ka.

2. Where PIE had a laryngeal (one of three consonants of uncertain value, represented in writing as *h, usually w/a numbered subscript) between two other consonants, Sanskrit has i, as in pitar 'father' (PIE *ph₂ter) or duhitṛ 'daughter' (PIE dʰugh₂ter)

3. Sanskrit merges PIE *r and *l to r in all positions.

This is just a handful of correspondences, but I'm not a Sanskritist and there's a lot of groundwork required to fit everything together.

As /u/ILoveNomads says, the details of the migration are muddy. The fact that some kind of migration happened is absolutely indisputable. Languages move with people, and it is clear that Indo-European languages moved to India. If someone is saying otherwise, they're lying.

Reposting from the same question asked a couple of months ago:

There's no disputing that the Indo-Aryan languages originated outside of South Asia and spread to the subcontinent from the northwest at some point before recorded history. Exactly when and where those languages came from taps into the wider debate on Indo-European origins, which is always a provocative topic, but I think at this point we can be reasonably sure that they originated in West-Central Asia and were brought to India via the Iranian plateau sometime in the Late Bronze Age. Genetic evidence suggests that the spread of the language also involved a fairly substantial movement of people.

Now, the details of how that linguistic/demographic shift took place is a lot more debatable and I don't think it fits anything you could call an "Aryan invasion theory". The concept of the Aryans as a prehistoric ethnic group actually originates in India with the Rig Veda, probably the most valuable source on how the Indo-European languages actually spread. However more recent readings of the Rig Veda characterise the arya as a social stratum rather than an ethnicity. They were set apart from the dasa by their nobility and superior religious practices, and notably not because of their language or ethnic descent. This obviously makes the idea that the Aryans were an external group that brought a language into South Asia with them less persuasive. Even if we do equate arya identity with speakers of Indo-Aryan, if it's a prescribed social status rather than a transmitted ethnic affiliation then it's entirely possible that the indigenous population adopted it and became 'Aryans', rather than being replaced by them.

The "invasion" part is even more problematic, as this evokes the idea of a cataclysmic military campaign by the Aryans that wiped out the preceding, indigenous Indus Valley Civilisation (IVC). This narrative is typical of early twentieth century explanations of prehistoric cultural change that are now generally seen as hopelessly simplistic and lacking any basis in fact. There is no material evidence of an Iranian culture steamrolling its way across northern India. Nor is there evidence of large-scale violence, battles, cities being burnt to the ground and the like. There isn't even anything in particular that says the IVC was "wiped out" by anyone – urbanism declined for sure, but there's a lot of continuity in the material culture of the IVC and post-IVC periods.

If I were to proffer a synthesis of what really did happen (and I should stress this is heavy on speculation), it would be that what we're seeing with the 'Aryanisation' of South Asia is similar to the process of Indo-Europeanisation in Europe. In both regions the populous but relatively egalitarian agricultural societies that flourished in the preceding period seem to have hit a sort of malaise at the end of the 3rd millennium BCE. This was perhaps related to a combination of deteriorating climatic conditions, social stresses following millennia of population growth, and the inherent limitations of Neolithic farming economies.

These conditions seemed to favour more mobile, pastoral existence, and a group of nomadic herders with distant origins in the North Pontic steppe took great advantage of this and spread widely across Eurasia. Their way of life was quite different to that of agriculturalists like the IVC: livestock was a source of tangible economic and symbolic wealth held by individuals, leading to the emergence of significant social hierarchies; their use of horses and chariots gave them an edge in raiding or small-scale warfare, and may have allowed to them set themselves up as patrons of sedentary farming villages; and their mobility gave them social connections across a wide area, probably another source of social prestige.

There would be no need for these nomads to violently conquer the existing agricultural societies of South Asia. They simply moved in and pastured in marginal areas with little value to farmers; maybe even grazed herds on their fields after the harvest. But you had a situation where the old order was stagnating, people were struggling to make a living the way they used to, and yet here was a group of newcomers with large, prosperous herds; intriguing new ideas about individual wealth and status; military superiority; prestigious goods from exotic locations; and a language that could be understood not just in your own village but across most of the known world. It stands to reason that the existing population would be tempted to adopt the language and customs of these newcomers, which I'd suggest was the crucible of the arya identity that crops up later in the Rig Veda. Over the centuries this prestige-driven cultural assimilation led to the complete replacement of the preceding (presumably Dravidic) socio-linguistic order with a new, Indo-Aryan-speaking one across much of Northern India.

(This is essentially a slight elaboration of David Anthony's theory in The Horse, the Wheel, and Language, which I'd highly recommend as further reading.)

Is there any evidence to suggest a non-Indo European substrate in Sanskrit?