A Persian victory at Gaugamela?

[Vinization]

The move that secured the Macedonian victory at Gaugamela - a massive charge straight into the Persian center, where Darius III was - was an immensely risky gamble for Alexander. Case in point, his manouver created a gap in his army's line, one which was exploited by a detachment of Persian and Indian cavalry. Thankfully for the Macedonian king, not only did Darius flee, but the enemy horsemen decided to loot his camp instead of turning around and and attacking his or Parmenion's contingents (the latter of which was in serious danger of collapsing) in the rear.

Suppose that Darius doesn't lose his nerve and decides it'd be better to die fighting instead of retreating a second time (or that he'd probably get murdered if he survived, whichever), while the cavalry that breached the Macedonian line attacks and routs Parmenion's troops. With the invaders' left flank neutralized, the entirety of the Persian right wing attacks the Macedonian center in the rear, forcing Alexander to flee or quite possibly killing him, given he was always in the thick of the fighting.

By the end of the day the battlefield is under Persian control, while the Macedonian army is either annihilated (certainly a possibility, given how far they were from home and how badly they were outnumbered), or retreating to its homeland. What happens next? Syria and Egypt are bound to be reconquered by the Achaemenids (the latter with some difficulty, perhaps, given how rebellious it was), but what about Anatolia, especially the western part of it? Could Alexander, assuming he survives, assemble a new army by the time Darius gets there? My guess is not, given how the Greek cities are almost certain to rebel once news about Gaugamela spread far enough. They revolted after Alexander died IOTL after all, and put up quite a fight.

Assuming the Achaemenids get their act together in the 320s BC, could they launch a retaliatory invasion of Macedonia and turn it into either a vassal or a satrapy, like how it was during the reigns of Darius I and Xerxes?

 

[Vinization]

How could the Celtic invasion of Greece be affected by this POD, particularly if Macedonia is invaded and conquered by Persia? Could Thrace and Macedonia develop a Celtic majority? What about Anatolia, considering they settled in Galatia (roughly where Ankara is, roughly) IOTL?

 

[Galba Otho Vitelius]

This is almost too big a POD to write about.

The Persian Empire had been through some tough times, but was reviving, as empires often get a second breath of wind. If they defeated Alexander, there is no reason they could have continued several centuries.

The Hellenistic kingdoms are all gone. I don't think the Roman Empire is butterflied away, but the Romans likely don't bother taking in Syria and Palestine (Egypt is too valuable for an empire to pass up).

 

[Xenophonte]

Well, these are too much pods that should happen simultaneous and complementary way to favour the Persians, that it's quite telling of how bad were the things for them...

Suppose that Darius doesn't lose his nerve and decides it'd be better to die fighting instead of retreating a second time (or that he'd probably get murdered if he survived, whichever), while the cavalry that breached the Macedonian line attacks and routs Parmenion's troops. With the invaders' left flank neutralized, the entirety of the Persian right wing attacks the Macedonian center in the rear, forcing Alexander to flee or quite possibly killing him, given he was always in the thick of the fighting.

First, for your initial assumption, would work, you would need an entirely different Darius to the one that IOTL already had fled from the battlefield, (at Issus) instead that (as you propose) to stay and fight. But, in your scenario, if Darius, would have had fled, he would have been either killed or captured by Alexander.
So, even if at difference to IOTL, the Persian cavalry would be a different (other Pod) one and disciplined enough as for continuing their attack and would be able to breach the Macedon line... It would be already too late giving that, for this time, the Great King would have already been either captured or killed which would cause the Persian army to demoralize and fled from the battlefield...

Now, say that with a different Great King and/or (if possible) that instead of commanding the Army, in persona, that the Persian King, would dare to risk and trust the command of his army to some skilled general, then the OTL winning Macedon move wouldn't be possible.
Which, if the battle would develop similarly to as was OTL, then a possible Macedon defeat would have, indeed, interesting consequences.
The possible scenarios would depend on the magnitude of the defeat and the Macedon losses and if Alexander would have been killed or if he would survive the defeat and thus being able to withdraw and ask/wait for reinforcements...
Anyway, I would expect that at least, some of the Greek Cities would attempt to rise in rebellion at the moment that the Macedon defeat would be known in Greece. Without mention that if such news would be followed by the one of the Alexander death, that the entire Hellas would probably (helped by Persian gold) be in rebellion against Macedonia.
Which, I'd think, that would force either to Alexander of his regent/self appointed successor, to either fall back to a more defensible position, to Lydia or even to the teritory of the Greek Asian Poleis (Caria, Ionia). Or to attempt to reach or accept any possible agreement offered by the Persians, that would either allowed them to salvage something and to deal with the menace more close to home.