Out-of-equilibrium critical dynamics of the three-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> gauge model along critical relaxat

We address the out-of-equilibrium critical dynamics of the three-dimensional lattice Z_{2} gauge model, and in particular the critical relaxational flows arising from instantaneous quenches to the critical point, driven by purely relaxational (single-spin-flip Metropolis) upgradings of the link Z_{2} gauge variables. We monitor the critical relaxational dynamics by computing the energy density, which is the simplest local gauge-invariant quantity that can be measured in a lattice gauge theory. The critical relaxational flow of the three-dimensional lattice Z_{2} gauge model is analyzed within an out-of-equilibrium finite-size scaling framework, which allows us to compute the dynamic critical exponent z associated with the purely relaxational dynamics of the three-dimensional Z_{2} gauge universality class. We obtain z=2.610(15), which significantly improves earlier results obtained by other methods, in particular those obtained by analyzing the equilibrium critical dynamics.