Large\bf Higgs pair production in association with a vector boson at $e^+e^-$ colliders in theories of higher dimensional gravity

The models of large extra compact dimensions, as suggested by Arkani-Hamed, Dimopoulos and Dvali, predict exciting phenomenological consequences with gravitational interactions becoming strong at the TeV scale. Such theories can be tested at the existing and future colliders. In this paper, we study the contribution of virtual Kaluza-Klein excitations (both spin-0 and 2) in the process $e^+e^- \to HHZ$ and $ e^+e^- \to HH\gamma $ at future linear collider (NLC). We find that the virtual exchange KK gravitons can modify the cross-section $\sigma(e^+e^- \to HHZ)$ significantly from its Standard Model value and allows the effective string scale to be probed up to 6.4 TeV. The second process is absent at the tree level in the standard model, and can therefore be used to put limits on the effective string scale of 7 TeV.