Executive Summary : | Cosmological observations have indicated that the Universe is expanding at an accelerated rate. In the standard model of cosmology, based on Einstein's equations, this acceleration is attributed to the presence of a dark energy component - called the cosmological constant. However, theoretical estimates of the energy density of this component do not agree with the observed value. Therefore the need arises for alternate explanations. One possibility is that Einstein's equations are incorrect and a plethora of phenomenological modified gravity models have been proposed in the literature. Clues that discriminate between these various models lie in the observations of large scale structure i.e., the observed pattern of matter distribution on the sky - galaxies, clusters, superclusters etc. In this proposal, we aim to theoretically track the formation of structure in a modified gravity models. In standard gravity, the governing equations are the continuity and Euler equations of hydrodynamics along with Poisson's equation for the potential. In the absence of external anisotropic stresses, in Einstein's gravity the potential that governs particle dynamics (Newtonian potential) and appears in the Euler equation is the same as the potential that appears in Poisson's equation (Curvature potential). This feature simplifies the equations and in spherical symmetry reduces them to simple second order Ordinary Differential Equations (ODEs). However, this structure breaks down in modified gravity models and in addition to the Euler and continuity equations, one needs to solve for two non-linear spatial equations for the potentials making the numerical scheme to solve the system more complex. Solving this complex system is the main aim of this proposal. |