Time-varying coupling strengths, nuclear forces and unification

We investigate the dependence of the nucleon-nucleon force in the deuteron system on the values of coupling strengths at high energy, which will in general depend on the geometry of extra dimensions. The stability of deuterium at all times after nucleosynthesis sets a bound on the time variation of the ratio of the QCD confinement scale to light quark masses. We find the relation between this ratio, which is exponentially sensitive to highenergy couplings, and fundamental parameters, in various classes of unified theory. Model-dependent effects in the Higgs and fermion mass sector may dominate even over the strong dependence of the QCD scale Λ. The binding energy of the deuteron also has an important effect on nucleosynthesis: we estimate the resulting bounds on variation of couplings.