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Noncommutative spectral geometry offers a purely geometric explanation forthe standard model of strong and electroweak interactions, including ageometric explanation for the origin of the Higgs field. Within this framework,the gravitational, the electroweak and the strong forces are all described aspurely gravitational forces on a unified noncommutative space-time. In thisstudy, we infer a constraint on one of the three free parameters of the model,namely the one characterising the coupling constants at unification, bylinearising the field equations in the limit of weak gravitational fieldsgenerated by a rotating gravitational source, and by making use of recentexperimental data. In particular, using data obtained by Gravity Probe B, weset a lower bound on the Weyl term appearing in the noncommutative spectralaction, namely $\beta \gtrsim 10^{-6}$m$^{-1}$. This constraint becomesstronger once we use results from torsion balance experiments, leading to$\beta \gtrsim 10^{4}$m$^{-1}$. The latter is much stronger than any constraintimposed so far to curvature squared terms.

Constraints on NonCommutative Spectral Action from Gravity Probe B and Torsion Balance Experiments