There are a lot of terms and concepts in regard to "the Aryans"; and to add to the confusion, they overlap linguistically, culturo-spiritually, and to a lessor extent: ethnically.
In the above link, you will find a maze of terms and ideas which basically boil down to "Indo-European" being a "language family" with a common linguistic origin. Amazingly, this "language family" extends from Iceland to Sri Lanka.
It should be noted that this tie-in would not include Mongol, Semitic, or Turkic peoples; all of whom expanded at a later time period. That should lessen the confusion a bit; and it should also be noted that the English, Spanish, Portuguese, and Arabic languages all have speakers among them who are from all of the races of the world. Now if we consider that most of the ancestors of the Icelanders lived in the Ice Age Middle East over 20,000 years ago; then this linguistic tie-in becomes less of a radical idea... at least believable.
We should never confuse "Persian" with "Arabic," even if most are Muslim. Despite the despotism of the Mullahs today, very few are "radical Islamists." After the proto-Norse moved on, ancient Mediterraneans occupied ancient Persia, perhaps followed by a long connection with India; but Arabic, Mongol, or Turkic influence was genetically small.
I once saw an image online of a Persian man, perhaps in his forties, wearing a Kaftan of some type; who looked like a Norwegian. Not just because of his blonde hair and blue eyes, but all of this facial characteristics were Nordic-like. He had a thick blonde beard, deep eyes, straight nose, pronounced forehead, etc. If he shaved his beard, and dressed in Western-style clothing, he could walk down any street in Scandinavia unnoticed. It should be noted that the Iranian president, Ahmadinejad, is of a particular Semitic-type, and not a typical Persian.
This linguistic category is regional, but tied into the larger language family. It is also referred to as the "Aryan languages." It's present geographic range extends from eastern Turkey, Iran, Afghanistan, most of India, and Sri Lanka; or in other words "the eastern Indo-Europeans languages." I'm trying to stick with the linguistic aspect of this; but there are all sorts of cultural, religious, and ethnic overlap since the days of the original Aryans.
This isn't to say that the "original Aryans" were the Ice Age proto-Norse. That would be an oversimplification of this. Apparently, the proto-Norse who stayed behind as the weather grew warmer, strongly influenced more eastern peoples as far as language. As far as "the Aryan invasion of India," certainly someone invaded and influenced them. As to who exactly they were, I don't really know. Perhaps a later Persian-type of Aryan. Many of them likely had light hair and eyes at that time; which may explain some of the old accounts. That seems as good a theory as any.
"Aryans" (see Aryan, Indo-Aryan, and Aryan race)
Could it be that the ancestors of Ice Age proto-Norse who remained in the Middle East long after the tribes had moved on, then merged with early Mediterranean peoples (to form the "original Aryans?"), whose much later homogenized descendants invaded India and influenced it (mainly linguistically)? They seemed to have strongly influenced their spirituality as well. This logical hypothesis would not exactly fit either the preference of a Germanic or an Indian nationalist or idealist. However, doesn't it seem more logical than what they have offered?
It should be noted that these hypothetical proto-Mediterranean-Norse "Aryan" invaders would have looked like most Europeans today. It should also be noted that the Persian people of today would only be partly, perhaps mostly, descended from these "original ancient Aryan people." This could also explain why certain Odinic concepts appear similar to some Hindu traditions. Wikipedia: The term Aryan originates from the Sanskrit word ārya, in origin an ethnic self-designation, in Classical Sanskrit meaning "honourable, respectable, noble."