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The quark mass dependences of light element binding energies and nuclearscattering lengths are derived using chiral perturbation theory in combinationwith non-perturbative methods. In particular, we present new, improved valuesfor the quark mass dependence of meson resonances that enter the nuclear force.A detailed analysis of the theoretical uncertainties arising in thisdetermination is presented. As an application we derive from a comparison ofobserved and calculated primordial deuterium and helium abundances a stringentlimit on the variation of the light quark mass, $\delta m_q/m_q = 0.02 \pm0.04$. Inclusion of the neutron lifetime modification under the assumption of avariation of the Higgs vacuum expectation value that translates into changingquark, electron, and weak gauge boson masses, leads to a stronger limit,$|\delta m_q/m_q| < 0.009$.

Varying the light quark mass: impact on the nuclear force and Big Bang nucleosynthesis