@Kastrahl
The Aryan migration/invasion, whatever you want to call it did happen. And its main reason why Indians speak an Indo-European language. https://en.wikipedia.org/wiki/Indo-European_languages
The Aryans or Proto-Indo-Europeans as they are called academically, spread from the Pontic steppe conquering Europe from the Old-Europeans, the Iranian plateau from the Elamites and the Indian subcontinent from the Dravidians. There are countless evidence of that ranging from archeological, linguistical to genetic evidence.
Concerning the Indian subcontinent, when the Indus valley collapsed the Aryans/Proto-Indo-Europeans took advantage of that and invaded the subcontinent imposing their language alongside their religion, they also established a caste system putting the Dravidians at the bottom.
Genetic evidence, both haplogroup and admixture seems to point out that most of Indo-Aryans' DNA come from these Pontic steppe invaders. Whom they share the paternal haplogroups R1a and R1b just like any other Indo-European speaker from around the world. Also half of Indo-Aryans' admixture is from the Pontic steppe which they call academically 'Steppe admixture'.
I could go on speaking forever, but you should just read the sources:
https://en.wikipedia.org/wiki/Proto-Indo-Europeans
https://en.wikipedia.org/wiki/Indo-Aryan_migration