  We extend the mimetic cosmology to models containing gauge invariant
$p$-forms. The $0$-form case reproduces the well-known results of the mimetic
dark matter, the $1$-form corresponds to the gauge field mimetic model while
the $2$-form model is the Hodge dual of the $0$-form model in $4$ spacetime
dimensions. We study the cosmological applications of the new gauge field
mimetic model and show that it generates an energy density component which
mimics the roles of spatial curvature. In the presence of the Maxwell term, the
model also supports the flat, open and closed de Sitter-like cosmological
backgrounds while the spatial geometry is flat for all three cases. We perform
the cosmological perturbations analysis and show that the model is stable in
the case of open de Sitter-like solution while it suffers from ghost
instabilities in the case of the closed de Sitter-like solution.
