Maybe a West Eurasian steppe empire conquering half of Europe and Northern India could be the closest thing to resembling a Indo-European empire(both by analogy and by linguistics) but it would require an early POD.The chances are very slim, but there are ways to make this happen... technically. The OP says that these countries are to be united (but doesn't specify when the unification must occur) and are to remain united until the present day. Given the amazingly long stretch of time we have to work with (from the Indo-European migrations up to the very recent past), I'm sure a scenario can be imagined where a sort of League of Nations arises that encompasses all Indo-European countries-- and then gradually evolves into a true federation. It would almost certainly include non-Indo-European countries as well, but if it includes all Indo-European ones, it technically meets the criteria of the OP. Also, let's keep in mind that with potential PODs going that far back, a scenario featuring an industrial revolution in (what we call) Antiquity would not be impossible at all. By the present day, there could simply be a world government, which unites all Indo-Europeans by default because it unites the whole planet. Never say never.
That said, a straight-forward 'empire' that somehow encompasses all Indo-Europeans from the start (or from any ancient time, really) and keeps them all united until the present day is not possible... except with absurd amounts of luck (to the point where probibility fails, and you're just messing with the outcome ASB-style).
Not happening. Too much of a distance for the groups to have any similarities to make a union possible. The only way it could work is with modern transportation and communication to counter natural barriers, but by this point, Europeans and west Asians are too different. Likewise, a world government is not happening. Europeans aren't subjecting themselves to a state where they're the minority. If said state encompasses India, then Indians are the majority. Go ask any European if they want their country run by a government on an entirely different continent.The chances are very slim, but there are ways to make this happen... technically. The OP says that these countries are to be united (but doesn't specify when the unification must occur) and are to remain united until the present day. Given the amazingly long stretch of time we have to work with (from the Indo-European migrations up to the very recent past), I'm sure a scenario can be imagined where a sort of League of Nations arises that encompasses all Indo-European countries-- and then gradually evolves into a true federation. It would almost certainly include non-Indo-European countries as well, but if it includes all Indo-European ones, it technically meets the criteria of the OP. Also, let's keep in mind that with potential PODs going that far back, a scenario featuring an industrial revolution in (what we call) Antiquity would not be impossible at all. By the present day, there could simply be a world government, which unites all Indo-Europeans by default because it unites the whole planet. Never say never.
Maybe a West Eurasian steppe empire conquering half of Europe and Northern India could be the closest thing to resembling a Indo-European empire(both by analogy and by linguistics) but it would require an early POD.
Not happening. Too much of a distance for the groups to have any similarities to make a union possible. The only way it could work is with modern transportation and communication to counter natural barriers, but by this point, Europeans and west Asians are too different. Likewise, a world government is not happening. Europeans aren't subjecting themselves to a state where they're the minority. If said state encompasses India, then Indians are the majority. Go ask any European if they want their country run by a government on an entirely different continent.
Honestly let's just ignore the strict requirement of conquering literally every Indo-European, if we limit ourselves to at least most of Europe and most of India and Persia I think it possible to have such an empire.I considered this idea ("Genghis Khan except from Ukrain instead of Mongolia", basically) -- but there's no obvious way I see that extending to Iceland etc., nor do I think an Empire of that sort would last long enough (at least not in an undivided state). That said, such an empire could be the historical ideal of "unification" that a later federation uses... a bit like how the proponents of the EU and European unification in general like to reference Charlemagne as their predecessor (e.g. the Charlemagne Prize).
In any case it's doubtful people would recognize this old kinship between Indo-European languages without modern linguistics
No you can't, states are not created by conscious decision of a couple people you can reasonably expect to act differently.No, not really. You could just go back to the Proto-Indo-European homeland and have the Proto-Indo-Europeans consciously decide right from the very start that every land they conquer becomes a part of a unified empire.
Is there any way for there to be a Pan-Indoeuropean country in which all of the native lands of the Indo-Europeans (from Iceland in the west to India in the east) are united into a single country and for that country to still exist today?
I never said Europeans were always going to dominate the world.You're basing your view on a lot of OTL factors. Considering the POD can literally go back to 4000 BC for this, I'd like to argue that you're being far too determinist.
-- Dissimilar groups not forming a union is just nonsense, because there can be lots of incentive to form unions. Economic interests, mutual defence, etc.
-- You say it requires modern transportation and communication to counter natural barriers, and I agree that such a federation would need 19th century tech at least, but then I explicitly suggested a scenario where tech advances more rapidly. Hardly implausible with a POD going that far back.
-- You assume Europeans will inevitably be dominant. There is no basis to assume that, when such ancient PODs are on the table.
-- You assume India is destined to be vastly overcrowded by the ATL's present day. I can easily see a world where India is the first region to industrialise (potentially long ago), and has long since passed through the post-industrial demographic transition by the ATL's present day.
In short, you are way too hung up on OTL, and projecting your OTL assumptions onta an ATL scenario where they may not be (in fact: are quite unlikely to be) valid.