Possible wormholes in $f(R)$ gravity sourced by solitonic quantum wave and cold dark matter halos and their repulsive gravity effect

In this paper, we present new generalized wormhole (WH) solutions within the context of $f(R)$ gravity. Specifically, we focus on $f(R)$ gravitational theories formulated in the metric formalism, with our investigation centered on a power-law form represented by $f(R) = \epsilon R^{\chi}$. Here, $\epsilon$ is an arbitrary constant, and $\chi$ is a real number. Notably, this form possesses the advantageous property of reducing to Einstein gravity when $\epsilon=1$ and $\chi=1$. To obtain these novel WH solutions, we establish the general field equations for any $f(R)$ theory within the framework of Morris-Thorne spacetime, assuming metric coefficients that are independent of time. By utilizing an anisotropic matter source and a specific type of energy density associated with solitonic quantum wave (SQW) and cold dark matter (CDM) halos, we calculate two distinct WH solutions. We thoroughly investigate the properties of the exotic matter (ExoM) residing within the WH geometry and analyze the matter contents through energy conditions (ECs). Both analytical and graphical methods are employed in this analysis to examine the validity of different regions. Notably, the calculated shape functions for the WH geometry satisfy the necessary conditions in both scenarios, emphasizing their reliability. This ExoM is characterized by an energy-momentum tensor that violates the null energy condition (NEC) and, consequently, the weak energy condition as well, in the vicinity of the WH throats. Furthermore, we investigated the repulsive effect of gravity and discovered that its presence results in a negative deflection angle for photons following null geodesics. Importantly, we observed that the deflection angle consistently exhibits negative values across all $r_0$ values in both scenarios, indicating the manifestation of the repulsive gravity effect.