CP-odd interaction of axion with matter

In the world with axion the precise measurement of gravitational force and check of the equivalence principle at small distances, $\lambda\sim 1cm$ and less, could provide an additional test of CP symmetry. Using the chiral approach, we connect the strength of CP-odd axion-nucleon vertex with CP-odd pion-nucleon coupling for color electric dipole moments of quarks as a low energy source of CP violation. Strong limits on CP-odd coupling $g_{\pi NN}$ coming from atomic electric dipole moments show that gravitational experiments are six orders of magnitude away from the sensitivity level needed to detect axion-mediated forces.