Greek verbs with initial #i+H4- from Arnaud Fournet (May 2017) *H4eH4- ‘to heal, guard’: (1)Hurrian a-tt- ‘to guard, protect’ (2) Greek ἰάομαι ‘to heal’ < *y-ā- (3) The question : why "ia" instead of "a" ?
Personally I find all this laryngealist madness highly unscientific. Some scholars use laryngeal phonemes as a jolly when there is something uncertain in the etymology of some word. These reconstructions are not only typologically unlikely, but also inconsistent with the initial, and brilliant, idea of "sonant coefficients" suggested by de Saussure. This usage of laryngeals is unfalsifiable, and should therefore be avoided. I think such reconstructions as *H₄eH₄ are simply wrong.
Concerning the Greek verb ἰάομαι, the etymology is quite uncertain. For sure, it cannot go back to a *y-a- because antevocalic /i/ in Greek evolved into an aspiration /h/ or, perhaps, into /dz/ in such forms as ζυγόν vs. Latin iugum. Moreover, knowing some basic Greek is important in dealing with IE etymologies. As you can easily see, ἰάομαι starts with a hiatus which very likely implies some lost consonant between the two vowels, i.e. either a /s/ or a /w/. Pokorny's dictionary mentions this word under the PIE root *eis which has a very vague semantics, so the etymology cannot be considered certain. But if the root is this, then the lost consonant must be the sibilant, and therefore the reconstruction as H₄eH₄, whatever we might think of it, is disallowed.
The origin of iáomai is unknown, but it seems as though the first two syllables could result from *iCa-, where C = a consonant that was lost in all forms of Greek before dialectal breakup, but after the older *j- glide disappeared or transformed.
Intervocalic -s- is one candidate for such a consonant: compare Greek heu- (heuō, heuein, etc.) "to singe" < *eus- (> Latin ūr- "to burn").
If so, there might be a connection with e.g. Welsh iach, Breton yac'h "healthy", since intervocalic -s- has disappeared in British Celtic as well. But this isn't an especially good match (for example, there is nothing in the Greek word that obviously corresponds to British Celtic -ch), so this is just a speculative connection.
I have a co-relation of sorts between *H4eH4- ‘to heal, guard’ and the Sanskrit term for "heal" , medicine, etc. However I have no correlation with the Greek term ἰάομαι ‘to heal’ < *y-ā- .
*H4eH4- ‘to heal, guard’ Hurrian a-tt- ‘to guard, protect’ Greek ἰάομαι ‘to heal’ < *y-ā- *H4eH4- ‘to heal, guard’
Sanskrit - To heal : भिषज् (भिषज्यति) bhiSaj The remedy: भेषजं, भैषज्यं, औषधं, रोगहं. MEDICINAL- (Having healing properties) औषधीयः -या -यं, Aushadhiiya भैषजः -जी -जं, भेषजीयः -या -यं, औषधोपयोगी -गिनी -गि (न्) Hurrian a-tt has a co-relation with Hindi - "aaTaa" ground wheat flower.During the fifties in the cities in India, private doctors who attended to patients in small private clinics, had assistants who ground minerals and herbs to powder to prepare medicinal syrups (jarabes). Not a historical linguistic co-relation but this is as far as I can go on the subject. The Academia.edu discussion on the topic has ended; I have seen no answers to Arnaud Fournet´s query.Perhaps I am the only one who attempted an answer , but not in the historical linguistic sense. It would be more in line with Cultures and interacting dialects and languages, over an enormous geographical area and an intervening period of six to ten thousand years BP.