Also remember that the left-right bend in the main branch is roughly based on solar activity. So you can see solar activity peaks (branch left) and minima (branch right).
Examples:
-Minoan warming ~2000 BC
-Bronze Age Collapse cooling ~1200-800 BC
-Roman warming until 500 BC
I have not yet studied it in detail, but I would not be surpised if mediterranean golden ages were heavily influenced by climate. Similarly for large invasions and migrations.