Exact solutions of the cosmological perturbations in a pressureless medium

We present integral-form exact solutions of the cosmological perturbations in a pressureless medium. The solutions include the background three-space curvature and the cosmological constant and are valid outside the Jeans scale, which is negligible compared to the horizon scale in a matter-dominated medium. Solutions are presented for recently introduced six different gauge choices, and we discuss the relations to Newtonian analysis. We identify the perturbed density variable in the comoving gauge, the perturbed velocity, and potential variables in the zero-shear gauge as having correct Newtonian correspondences. On subhorizon scales, behavior of the fluid and potential variables in the uniform-expansion gauge also show a correct match with the Newtonian results.