Abstract

We investigate the evolution of linear density contrasts obtained with respect to a homogeneous spatially flat Friedman-Lemaître–Robertson–Walker background by solving the density contrast equations governed by Newtonian and MONDian force laws using symmetry-based approach. We find eight-parameter Lie group symmetries for the linear order density perturbation equation for the Newtonian case whereas the density contrast equation follows only one parameter Lie group symmetry in MONDian case. We use Lie symmetries to find the group invariant solutions from invariant curve condition. The physical features of the evolution for various mode of density contrast with respect to the global cosmic background density in homogeneous isotropic cosmological models have been investigated using analytical group invariant solutions along with their numerical solutions. An account for cosmological density contrast and mass fluctuation also have been provided. We also have shown that the MONDian force law generates higher amplitudes in the density fluctuation, results in a more rapid structure formation that cannot be possible under the Newtonian force law.