Hi! Yes the expansion theory is historically accurate. Initially, it was believed that a horde of white people invaded and conquered India, hence the "invasion theory" (the British used this idea to justify their own colonization of India along terrible racist lines). However, this has changed--the model is now understood as a migration out of the Pontic Caspian Steppe region, it was not hordes of conquering people but rather something more along the lines of small bands that engaged in the practice of elite transfer (and we have the archaeology to prove their migrations out of the Pontic Caspian Steppe). In India this is totally rejected because it is still presented as an invasion, and the OIT theory was developed as a substitute explanation. India gains independence in 1947 and needs to construct an identity for itself, and they started by twisting the Indo-European migration along nationalistic and religious lines. Within India this model is accepted, but outside of that country no self-respecting scholar takes the OIT interpretation seriously because it has several major pitfalls, one of the major ones being that the remains of horses (which we know the Indo-Europeans used extensively) come from strata which are too late in time to correlate it to these groups leaving India. Additionally, the linguistics and the dates given for them do not match if the Indo-Europeans had originated on the subcontitent.

Sources: The Horse, the Wheel and Language by D. Anthony, and Empires of the Silk Road by C. Beckwith.