Novel Relativistic Wormhole Solutions in Extended Symmetric Teleparallel Gravity Sourced by Holographic Dark Energy

In connection with the importance of gravity with regard to the dark energy problem and different wormhole (WH) models, we have developed WH models supported by Holographic dark energy (HDE) in the background of gravity. The gravitational field equations for the WH model and associated energy conditions have been developed in the framework of gravity. We have determined the exact WH solution to the gravitational field equations employing the HDE equation of state (EoS) in the linear model of WH, where the linear function is employed. Further, numerical solutions to the field equation in the quadratic model of WH have been obtained considering . We have investigated features of the shape function and energy conditions of the WH for different sets of observational data representing phantom‐type or quintessence‐type HDE for both the linear and quadratic models. The influence of parameters on the attributes of the shape function and energy condition has been depicted graphically and analyzed in detail for all the cases. It has been observed that phantom‐type HDE supports the configuration of WH in case of the linear model, whereas physical WH exists for both phantom‐type and quintessence‐type HDE in case of the quadratic model in the background of gravity. Based on observational constraints of HDE, the WH models predict the existence of a critical value of parameters representing the strength of the energy‐momentum tensor, i.e., and beyond which WH becomes non‐physical.