Non-singular bouncing cosmology in f ( Q , L m ) gravity with nonlinear matter coupling

In this paper, we investigate a non-singular bouncing cosmology within the framework of [Formula: see text] gravity. We adopt the functional form [Formula: see text], which combines a linear non-metricity contribution, a nonlinear mattergeometry coupling, and an effective cosmological constant. Then, to construct the bounce analytically, we employ a symmetric scale factor [Formula: see text] that naturally connects a contracting phase with a subsequent expansion in a smooth and regular manner. The resulting cosmological evolution exhibits the characteristic features of a viable bounce scenario. In particular, the scale factor remains finite for all cosmic times, the Hubble parameter passes through zero with [Formula: see text], and the deceleration parameter shows a brief super-accelerated phase in the vicinity of the bounce. Further, the effective equation of state (EoS) parameter [Formula: see text] briefly enters the phantom regime ([Formula: see text]), leading to a violation of the null energy condition, which is required to evade the initial singularity. The strong energy condition is also violated near the bounce, while the dominant energy condition remains satisfied throughout the evolution, ensuring physical consistency of the model. These results indicate that the proposed [Formula: see text] scenario presents a consistent realization of a non-singular cosmology driven by nonlinear mattergeometry effects.