"Cultural decline" is questionable. There is no objective criterion to judge and compare different cultures. There was art and architecture, and you can never say that the art of one culture is inferior to that of another.
But decline of science is a fact, and it happened on the whole territory of the former Roman empire, both in the West and in the East, at the same time. People lost interest to science.
Sciences like mathematics and astronomy were formally prohibited by an edict of Justinian.
Schools in Athens and Alexandria were closed, and the last few philosophers were forced to emigrate (to Persia). At least one of them was later permitted to come back, under the condition that he will not teach.
Cosmas Indicopleustes wrote his Christian Topography in 6-th century, where he proved that the Earth is flat, and this book was very popular during the Dark Age. This was 4 centuries after the great Ptolemy!
On my opinion, the reason of all this is the spread of Christianity. And suppression of all independent thought as a result.
EDIT. Edict of Justinian which closed the school in Athens and exiled philosophers
was in 565. Museion in Alexandria was destroyed by the Christian mob in the previous century. Cosmas wrote in in the same time (550). Gibbon in Decline and Fall of the Roman empire, Chap. XL, wrote:
The Gothic arms were less fatal to the schools of Athens than establishment of a new religion, whose ministers superseded the existence of reason, resolved every question by an article of faith, and condemned the infidel or skeptic to eternal flame. In many a volume of laborious controversy they exposed the weakness of the understanding and the corruption of the heart, insulted human nature in the sages of antiquity, and proscribed the spirit of philosophical inquiry, so repugnant to the doctrine, or at least to temper of a humble believer.
EDIT 2. Here is a more modern source: Ch. Freeman, The closing of Western mind. The rise of faith and the fall of reason, A. F. Knopf, NY 2003.