Spectral action beyond the weak-field approximation
  The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even dimension. 
B. Iochum, C. Levy, D. Vassilevich
hep-th math-ph math.MP