See also: https://en.wikipedia.org/wiki/Kurgan_hypothesis#/media/File:IE_expansion.png
Map of Indo-European expansion 4000–1000 BC, according to the Kurgan hypothesis. Even within the Kurgan hypothesis, there is considerable uncertainty, mainly depending on assumptions about the Tocharians, the Corded ware culture, and the Beaker culture. The central purple area is supposed to show early Yamna culture (4000–3500 BC); the dark red area could show expansion to about 2500 BC; and the lighter red area,expansion to about 1000 BC.