Does extra-dimensional physics destabilize our universe's fundamental constants?

In Randall-Sundrum braneworld models, a scalar field called the radion sets the size of the extra dimension and explains why gravity is so weak compared to other forces. This study maps out exactly when that radion becomes tachyonically unstable — essentially when it wants to roll away from its stable value — finding that ordinary positive-trace matter on the brane can destroy the mechanism that solves the hierarchy problem, while negative-trace matter leaves it intact. The result ties extra-dimensional stability directly to the matter content of our universe and extends to f(R) gravity theories relevant during inflation.