Cultural transmission lead to potentially-immortal ideas - with a correspondingly greater scope for cumulative adaptive evolution.
Cultural transmission also produced much larger idea pools - with more variation within each pool.
Before culture, ideas could only recombine with other ideas inside the same head. With culture, ideas could recombine with ideas from other individuals. The larger idea pools provided much greater scope for ideas to recombine. For the first time, ideas from men could recombine with ideas from women. Ideas from experienced individuals could combine with ideas from inexperienced ones.
The enlarged idea pool became a meme pool. With greater diversity and more scope for outcrossing this resulted in an enlarged human brain (with more space for memes) and the invention of science, technology and the internet. The memes then set about constructing a diverse range of new bodies and minds for themselves.
Richard Dawkins has said that stars might "go information" - rather than "go supernova". The existing cultural explosion might well continue to build until this happens.