I guess this has been attempted before, but I'd like to hear your comments.
Mussolini was a Hitler-fanboy and did declare war upon the Allies during the Fall of France, hoping that the war would end soon and his declaration of war would secure Italy some gains.
What if he didn't? What if he decided to stay neutral?
The Germans still take out France more or less like in OTL. Italy keeps its colonies and there is no N. Africa campaign. The British need to fight the Germans only over the Channel in the next couple of months.
Mussolini never invades Greece. Metaxas probably does not allow the British to station themselves in Greece.
Do the Germans still go after Yugoslavia?
Without a Greek campaign the Germans perhaps launch Barbarossa 1-2 weeks earlier and possibly come a bit closer to Moscow, before being stopped by fresh Soviet troops and the weather. Without the Italian contribution there are some less Axis forces in the Eastern front.
The biggest butterflies happen however due to no North African front. This releases additional forces both for the Germans and the British.
The British have more aircraft at home, possibly leading them to being more aggressive in bombing raids against German occupied France. Without any battles having to be fought in the Med, the British also have more resources to throw into the Battle of the Atlantic. Perhaps we may see earlier Murmansk bound convoy battles, as more ships and material will be available to aid the Soviets. Extra resources can also be sent to Far East Asia with major butterflies coming for the Japanese. No Taranto air raid hitting the Italian Navy may also have butterflies in naval doctrine in the Pacific War and perhaps even the entire Pearl Harbor operation?
The Germans have a couple of extra divisions and a load of trucks available for the Eastern Front. They can however also trade freely with Italy. Could this become a major boost for the Italian economy? Do the Germans have access to more scarce resources, than in OTL through Italy?
The British Med strategy is toast in such an ATL. The Allies will have to invade France with a cross channel invasion. Greece and Italy are neutral. Even if Yugoslavia is in German hands, making a landing in the Adriatic Sea is suicidal, due to the distances involved from Allied held bases in N. Africa. Can the Allies try a cross channel invasion in 1943, without having to waste men and resources in a N. Africa campaign? Vichy controlled N. Africa still gets invaded, but the Germans probably have no chance of defending it. Perhaps we may see a simultaneous invasion of Northern and Southern France with more forces devoted to the South than in OTL?
Has a full TL ever been written on this basis?