A study on the geometric configuration and stability of wormholes in symmetric teleparallel gravity influenced by dark energy and rotational velocity profiles

Abstract This study explores the characteristics of wormhole geometries within the framework of symmetric teleparallel gravity, specifically $$\mathcal {F}(\mathcal {Q})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity. By integrating holographic and mixed dark energy density profiles, we derive exact solutions for wormholes. The analysis focuses on the geometrical aspects of these wormholes, employing rotational velocity to formulate the redshift function and using dark energy density profiles to establish the shape function. By selecting specific parameter values, we show that the derived wormhole solutions meet the flare-out condition within an asymptotic background. We also evaluate the energy conditions, with particular emphasis on the null energy condition at the wormhole throat. Our findings indicate that the coupling constant $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> significantly influences the violation of energy conditions, especially the null energy condition, accompanied by graphical representations. Additionally, the research examines key features of the wormholes, such as complexity factor, anisotropy, exoticity, and embedding diagrams.