It is thought to be the Welsh Atlantis, a lost land at the bottom of the bay. For at least 800 years, tales have been told of the legend of Gwaelod, but little evidence has been found to support it.
The legend may be based on historical fact, according to a report.
The discovery was made by Simon Haslett, a professor of physical geography atSwansea University, and David Willis, Jesus professor of Celtic at the University ofOxford.
While he was a visiting fellow at Jesus College, Oxford, Haslett went in search of lost islands and found that the two islands were clearly marked on a map.
The earliest complete map of the British Isles is thought to be the document. Their findings have been published.
The two islands are about the same size. There are two islands, one off the coast of Aberystwyth and the other north of Barmouth.
The surveying tools they would have had at that time make the map extremely accurate.
The Black Book of Carmarthen states that there is a lost land on the two islands.
The Black Book's account was important to anchoring the story in Welsh myth, according to a Welsh folklore expert.
The Black Book of Carmarthen is said to have its beginnings around 1200.
Drawing on previous surveys of the bay and understanding of the retreat of glaciers and silt since the last ice age about 10,000 years ago, they were able to suggest how the islands may have come into existence and then vanished again.
The evidence for the islands is in two strands.
The coordinates recorded by Ptolemy suggest that the coastline may have been further west than it is now.
The evidence presented by the map supports the existence of two islands in the bay.
Folk tales of being able to walk between lands now separated by sea could be related to rising sea levels.
It is possible that legends of sudden flooding, such as in the case of Gwaelod, may have forced the population to abandon their homes.
Wood said that people now want to find a way of explaining things.
Celtic romanticists want to find meaning and a belief system that makes sense of the current hardship.
He warned that his findings could have an impact on the future.
He said that the processes weren't done just once.
It has been suggested that people living around Cardigan Bay could become some of Britain's first climate change refugees within our lifetimes.