Earth and the Core worlds are bright, shiny and new. They have developed infrastructure and a high standard of living. The Frontier, Not so much.
The Terro Human Alliance depends on the following pieces of unknown technology.
Everything else can be handwaved. (Life support, carniculture, space building, and so on)
Earth Discoveres Abbot Lift-and-Drive and Dillingham Hyperdrives at very nearly the same time.
There is a diaspora of people fleeing a cyberpunk like hell hole on earth.
Then a Terran Authority takes over and makes things nice, or else.
The Alliance is control freaky. Allows no other power to challenge it. TA Troopers Spend a lot of time chasing and mashing rebels and pirates.
Smugglers, Rebels and Pirates keep flying.
In name, form and Theory, an Alliance of Core Worlds who have banded together for mutual defense, trade and diplomacy. In reality, nice PR for the Terran Authority issuing orders and the Core Worlds saluting sharply and proceeding.
The Democratic forms give the residents of the core worlds enough cover to feel like the Alliance is really "The Good Guys" and to ignore reports of injustices and massacres as "extreme" and "one sided reporting/interpretation."