Dear sweta,
I think the reason that you got Au-Au bond varying from 2.68-2.88 Angstrom is that you optimzed a supercell of Au lattice. The one 2.88 is obtained from the unitcell.
In principal, even if you use a supercell to do the optimization, the Au-Au bond should be the same, since every Au atom has the very same environment. However, in numerical calcualtions, the program do not consider the symmetry of the system. So, you got your results.
With best regards,
Guangping