By the 9th century, Catalan had evolved from Vulgar Latin on both sides of the eastern end of the Pyrenees, as well as the territories of the Roman province of Hispania Tarraconensis to the south. From the 8th century onwards the Catalan counts extended their territory southwards and westwards at the expense of the Muslims, bringing their language with them. This process was given definitive impetus with the separation of the County of Barcelona from the Carolingian Empire in 988.
What gave momentum to the Catalans moving into Muslim territories?
the separation of the County of Barcelona from the Carolingian Empire