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In this paper, we investigate a ( 1 + 3 ) -dimensional static Friedmann-Robertson-Walker (FRW) space-time, pierced by a cosmic string. Our analysis begins with a detail study of the geodesic motion of photon rays in this curved background, focusing on the behavior of the associated effective potential. This allows us to understand how the cosmic string and curvature of space-time influence the trajectories of light rays. Moving beyond ray optics, we explore wave optics by solving the covariant Helmholtz equation in this gravitational setting. By transforming the resulting radial equation into a Schrödinger-like form, we extract an effective potential and derive a frequency-dependent refractive index. This refractive index shows the combined effects of the cosmic string and the curvature parameter, showing their influence on the wave propagation. Furthermore, we extend our study to a ( 1 + 2 ) -dimensional space-time with disclinations, where we analyze the wave optics phenomena. Through the Helmholtz equation in this lower-dimensional case, we determine the refractive index and discuss how it is affected by the geometric parameters of this lower-dimensional space-time. Through both geometric and wave optics approaches, our work provides a comprehensive understanding of how topological defects and curvature impact geometric and physical optics in curved space-time of three- and four-dimensions.
Ahmed et al. (Tue,) studied this question.