Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant

Abstract In this paper, a specific solution to the second-order cosmological perturbation theory is given. Perturbations are performed around any Friedmann–Lemaître–Robertson–Walker spacetime filled with dust and with a positive cosmological constant. In particular, with a possibly non-vanishing spatial curvature. The adopted symmetry condition allows us to simplify the equations, leaving us with a great deal of freedom to choose the density distribution. In the result, we get a relatively simple metric of an inhomogeneous cosmological model, which will give a perfect tool for studying the influence of the local inhomogeneities onto the cosmological observables.