The Breathing Vacuum

3. Final Classical VTF Lagrangian (Bosonic Sector)

\boxed{
\mathcal{L}_{\text{VTF}} =
\underbrace{\frac{1}{2} f(T) \partial_\mu T \partial^\mu T}_{\text{kinetic (gravity-dressed)}}
- \underbrace{\lambda (T_{\text{max}} - T)^2 \left[1 - e^{-\alpha (T_{\text{max}} - T)}\right]}_{\text{potential}}
+ \underbrace{\frac{1}{2} f(T) R}_{\text{gravity}}
- \frac{1}{4} F_{\mu\nu} F^{\mu\nu}
}

Wait — where’s the gauge field? See below.