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The noncommutative spectral action extends our familiar notion of commutativespaces, using the data encoded in a spectral triple on an almost commutativespace. Varying a rather simple action, one can derive all of the standard modelof particle physics in this setting, in addition to a modified version ofEinstein-Hilbert gravity. Thus, noncommutative geometry provides a geometricinterpretation of particle physics coupled to curvature. In this letter we useobservations of pulsar timings, assuming that no deviation from GeneralRelativity has been observed, to constrain the gravitational sector of thistheory. Thus, we directly constrain noncommutative geometry, a potential grandunified theory of physics, via astrophysical observations. Whilst the bounds onthe coupling constants remain rather weak, they are comparable to existingbounds on deviations from General Relativity in other settings and are likelyto be further constrained by future observations.

Constraining the Noncommutative Spectral Action via Astrophysical Observations