  We analyse the aging dynamics of the one-dimensional Fredrickson-Andersen
(FA) model in the nonequilibrium regime following a low temperature quench.
Relaxation then effectively proceeds via diffusion limited pair coagulation
(DLPC) of mobility excitations. By employing a familiar stochastic similarity
transformation, we map exact results from the free fermion case of diffusion
limited pair annihilation to DLPC. Crucially, we are able to adapt the mapping
technique to averages involving multiple time quantities. This relies on
knowledge of the explicit form of the evolution operators involved. Exact
results are obtained for two-time correlation and response functions in the
free fermion DLPC process. The corresponding long-time scaling forms apply to a
wider class of DLPC processes, including the FA model. We are thus able to
exactly characterise the violations of the fluctuation-dissipation theorem
(FDT) in the aging regime of the FA model. We find nontrivial scaling forms for
the fluctuation-dissipation ratio (FDR) X = X(tw/t), but with a negative
asymptotic value X = -3*pi/(6*pi - 16) = -3.307. While this prevents a
thermodynamic interpretation in terms of an effective temperature, it is a
direct consequence of probing FDT with observables that couple to activated
dynamics. The existence of negative FDRs should therefore be a widespread
feature in non mean-field systems.
