Gauge invariant treatments of the second order cosmological perturbation in a
four dimensional homogeneous isotropic universe filled with the perfect fluid
are completely formulated without any gauge fixing. We derive all components of
the Einstein equations in the case where the first order vector and tensor
modes are negligible. These equations imply that the tensor and the vector mode
of the second order metric perturbations may be generated by the scalar-scalar
mode coupling of the linear order perturbations as the result of the non-linear
effects of the Einstein equations.Comment: 5 pages, no figure. RevTeX; short letter version of gr-qc/0605108;
some details of explanations are adde