Dear all,
Regarding the into India versus out of India conversation, I would suggest looking at the latest DNA study on the topic. It is the most recent and most comprehensive study to date, from this year. Here is a general article noting its conclusions:
For the scientific study itself:
https://www.biorxiv.org/content/biorxiv/early/2018/03/31/292581.full.pdf
The following map from the article summarizes the main population movements found with the current data. The map also appears in:
Reich, David. 2018. Who We Are and How We Got Here: Ancient
DNA and the New Science of the Human Past. New York:
Pantheon Books. Chapter six is about India. Reich, at Harvard, is
maybe the leading scientist in this field.
The main thing for this discussion in the map is the Indian
Cline, which shows a movement into India from Inner Asia between
2000 BCE and 1700 BCE. Notice also how those who are here
identified as the Yamnaya pastoralists migrated west into Europe,
and east and south into South Asia. Genetics, of course, is not
the same as language, but it is striking that the period from 2000
to 1700 BCE coincides perfectly with the dates that have been
estimated for the arrival of the self-styled Aryas into South
Asia.
The map has high resolution, so it can be amplified. Here it is: