A cosmological lower bound on the neutron electric dipole moment

We argue that in a wide class of grand unified theories diagrams similar to those generating baryon number in the early universe also contribute to renormalization of the CP-violating θ parameter of QCD and hence to the neutron electric dipole moment d_n. We then use the apparent baryon-to-photon ratio ( n_B n_γ) ≳ 1.3 × 10^-10 to deduce an order-of-magnitude lower bound on the neutron electric dipole moment: d_n ≳ 3 × 10^-28 e cm. Conversely the present experimental upper limit on d_n implies ( n_B n_γ) ≲ 6 × 10^-7. We find as a corollary that there is not much scope for entropy generation after the creation of the baryon-antibaryon asymmetry in the very early universe.