This is the hypothesis proposed by Liuvob Golovanova in the latest issue of Current Anthropology, according to Science News.
Golovanova's team has found two different volcanic ash layers in the Neanderthal site of Mezmaiskaya, in the North Caucasus, the first one is dated to c. 45 Ka ago and the second one to c. 40 Ka ago. This one seems to have sealed the fate of Neanderthals in the Caucasus.
Some time later, c. 38-37 Ka ago, items that are mostly associated with Homo sapiens, such as perforated shell ornaments, bone points and other items, appear at the site.
A similar situation is found, as far as I know, in the not too distant site of Kostenki, in southern Russia. The 40 Ka eruption is also associated with the cold episode known as HE4 and has been related to the expansion of Aurignacian culture in SW Europe.
However it must be noted that in the same issue, geologist Biagio Giacio, challenges Golovanova's account, mentioning the presence of artifacts under the ash layer in several Mediterranean locations. I presume that these are the same sites that Julien Riel-Salvatore has been digging in Southern Italy, of Uluzzian culture.
Riel-Salvatore stands today at his blog by his published claims of Uluzzian being a Neanderthal industry, mostly because of the existence of a Mousterian (probably Neanderthal) buffer in Central Italy arguably preventing Sapiens influences from arriving, but other researchers have already proposed that it is of H. sapiens manufacture because of it srather unmistakable Upper Paleolithic style, including bone tools (unknown to have been ever made by Neanderthals), and specially the presence of perforated decorations.
The debate continues.
Ref. L.V. Golovanova et al. Significance of ecological factors in the Middle to Upper Paleolithic transition. Current Anthropology. Vol. 51, October 2010, p. 655. doi:10.1086/656185.