I fail to understand how the Rigvedic society can be connected to this DNA research. Rigveda never mentions anything beyond the Punjab/Swat/Haryana region in any of the hymns. The flora and fauna mentioned in it is also exclusive to this region. Lastly there is no mention of an ancient homeland both in Rigveda and Avesta.
Here we go: https://www.discovermagazine.com/planet-earth/chariot-racers... - make of that what you will.
https://www.cambridge.org/core/journals/radiocarbon/article/...
- no horse remains or equestrian objects have been found, anywhere in India for this time period
- solid wooden wheels (shown in the reconstruction) are too heavy for horses to draw, for which spoked wheels were developed in the Steppe
- the shape of the yoke that would be tied to the animals is straight, the way ox carts have, like Harrapan ox carts. By contrast, yokes for horses are curved, to match the animal's posture.
Edited to add: there are basically no migration stories in _any_ indo-european mythological cycles or oral traditions. That's not evidence that there wasn't spread through, migration or invasion, but it does indicate that it was a gradual process that wouldn't have been particularly noticeable in any one life time.
The problem of IE is of course very abstract, while the problem of, e.g., Celts is much more concretely paradoxical (continental and island Celts share the language family but not a lot of archaeology and a dubious amount of genes). However, it is still a more or less commonly accepted fact that at some point in the past PIE peoples spread like wildfire, bringing their dialects, genes, and culture to a very large area, and it is of huge historical interest to know where they started from.
The fact the IE epic and mythological traditions have zero memories of all this, I would say, is interesting but does not prove or disprove anything.
How much do English-speakers today know about the events in early 10th century France that eventually led to English becoming a sort of pidgin French, full of words like "eventually" and "sort" that didn't exist in Beowulf? How much effort do they typically devote to passing on traditions about Æthelwold's challenge to Edward the Elder in Wessex?
And that's after 1100 years of a literate, mostly settled culture with libraries that contain physical books from that time, in a culture that values that kind of factual knowledge of history, rather than more practical sorts of knowledge such as how to properly worship Agni to gain his favor and which plants to poison your arrows with.
Oral tradition can preserve knowledge to an astounding degree. There are songlines, as I understand it, that record the geography of landforms that have been undersea since the Ice Age (https://www.scientificamerican.com/article/ancient-indigenou... roughly the same time as the Proto-Indo-European culture). But it is hardly surprising when it is silent on a topic we wish we knew more about.
Irish have migration myths.
So do Greeks (probably a bit more localized intra-Balkan movement, though).
To be fair IE migrations were very long ago. It’s not inconceivable that oral myths might have been preserved for several thousand years and yet we might know nothing about them.
> wouldn't have been particularly noticeable in any one life time
Probably not true. At least genetic evidence points otherwise. IIRC we’ve found individuals as far as Britain who were closely related (a couple of generations) with remains found in the steppes. At least some elite groups were very closely related paternally and moved very fast across Europe.