Estimating Gravitational Redshift in Galaxy Clusters and Voids Using Hernquist and Tophat Density Profiles

Cosmic voids happen to occupy most under dense regions of the universe. They can, therefore, be used to test our theories of structure formation and cosmology. By assuming a density profile and using it to obtain the gravitational potential, the gravitational redshift is computed. The effect is compared in two profiles of clusters and voids. From the computations, the gravitational redshift in clusters is higher than that in voids, implying that if the effect is to be considered in voids, a larger survey is required. The radii used are 20 Mpc and 1 Mpc for voids and clusters respectively.