Rational Buddhism is that part of the purported teaching of the Buddha that is logical and consonant with the modern scientific view. Surprisingly a large section of the Buddha's teeaching, as is now available in the ancient compilations, inclding most of its core teachings, is surprisingly rational. The Buddha lived in the pre-sientific age and many of its beliefs involved concepts and places that could not be empirically verified. They were in the nature of beliefs about the world as appeared to explain the universe but could not be empirically verified. The Buddha used some of these beliefs where they could be used to inculcate the values he was trying to promote.
The Buddha seems to have accepted the cosmological views then prevailing. This involved the existence of heavens and hells. Later Buddhism expanded these extra-terrestral to cover some 32 planes of existence ranging from the most severe hells (niraya) to sublime divine realms (Brahmaloka). The inhabitants of these worlds, particulaly the devas (usually translated as 'gods') who inhabited the heavens were seen as being able to communicate with humans. This was particularly to case of the devas of the Vedic texts who could be induced to partake of the meat obtained in the various sacrifices. The Buddha did not advocate the Brahmanicl sacrifices but the devas figure in many discourses (suttas) attributed to the Buddha.
Anther contentious area of traditional Buddhist belief is the doctrine of rebirth or transmigration. For instance there are references to rebirth in most of the suttas in the Pali Canon which is basis of Theravada Buddhism. Some Buddhist scholars e.g. S G. Jennings have argued that theis doctrine is not part of the Buddha's core teaching. It was a belief in later Vedic thinking in the period prior to that of the Buddha, and the Buddha could have used it to induce people to follow is rather austere moral code. Thus people could be induced to do what is right by the promise of rebirth in heaven and not to do what is wrong by belief in hell.