Planck-Scale Physics and Solutions to the Strong CP Problem without   Axion
  We analyse the impact of quantum gravity on the possible solutions to the strong CP problem which utilize the spontaneously broken discrete symmetries, such as parity and time reversal invariance. We find that the stability of the solution under Planck scale effects provides an upper limit on the scale $\Lambda$ of relevant symmetry breaking. This result is model dependent and the bound is most restrictive for the seesaw type models of fermion masses, with $\Lambda < 10^6$ GeV. 
Z.G.Berezhiani, R.N.Mohapatra and G.Senjanovic