  Primordial SU(2) gauge fields with an isotropic background lead to the
production of spin-2 particles during inflation. We provide a unified formalism
to compute this effect in all of the inflation models with isotropic SU(2)
gauge fields such as Gauge-flation and Chromo-Natural inflation with and
without spectator axion fields or the mass of the gauge field from the Higgs
mechanism. First, we calculate the number and energy densities of the spin-2
particles. We then obtain exact analytical formulae for their backreaction on
the background equations of motion of SU(2) and axion fields in (quasi) de
Sitter expansion, which were calculated only numerically for one particular
model in the literature. We show that the backreaction is directly related to
the number density of the spin-2 field. Second, we relate the number density of
the spin-2 particles to the power spectrum and the energy density of the
gravitational waves sourced by them. Finally, we use the size of the
backreaction to constrain the parameter space of the models. We find that the
tensor-to-scalar ratio of the sourced gravitational waves can at most be on the
order of that of the vacuum contribution to avoid a large backreaction on
slow-roll dynamics of the gauge and axion fields in quasi-de Sitter expansion.
