Inflationary solution to the strong CP and μ problems

We show that the vacuum expectation value of the inflaton at the Peccei-Quinn axion scale can generate the supersymmetric Higgs mass μ term. This provides an inflationary simultaneous solution to the strong CP problem and the μ problem of the minimal supersymmetric Standard Model, and gives a testable prediction for the μ parameter: μ2≈(0.25-0.5)m02, where m0 is the soft Higgs scalar mass. Our model involves a very small Yukawa coupling of order 10−10, which could originate from an extra-dimensional scenario or type I string theory.