Not something you read about every day. A fairly technical account posted by Don Ringe at Language Log. It’s fascinating to see how these linguists work backwards and piece together a plausible history of language.
Proto-Indo-European (PIE) was a single language for which a complex grammar and an extensive vocabulary can be reconstructed; for a sketch of PIE see e.g. Ringe 2008:4-66. It follows that the speakers of PIE must have occupied a comparatively small territory. The idea that PIE might once have been spoken over most of Europe isn’t just unlikely; it’s impossible, because it’s so extravagant a violation of the UP. Exactly when and where PIE was spoken will probably be debated forever, but David Anthony presents an overwhelmingly strong case that it must have been somewhere in the steppes north of the Black and Caspian Seas around 4000 BCE (Anthony 2007; see also Mallory 1989). Much of his case is based on incontrovertible linguistic evidence. For instance, the fact that a word for ‘horse’ is solidly reconstructable for PIE (with reflexes in all the earliest-attested branches of the family, including Anatolian) rules out Mesopotamia, Anatolia, and any forested part of Europe as the area where PIE was spoken; the fact that words for ‘wool’, ‘yoke’, and ‘thill’ are also reconstructable for PIE, and that a word for ‘wheel’ is reconstructable for the last common ancestor of all the non-Anatolian branches of the family, eliminates any date much earlier than 4000 BCE. Later dates are eliminated by the fact that, by the time we have records of them, Hittite, Vedic Sanskrit, and Greek are so different from each other that they must have been diverging for two millennia or so.