Energy conditions of bouncing solutions in quadratic curvature gravity coupled with a scalar field

In this paper, we examine the validity of classical energy conditions in nonsingular bouncing cosmological solutions arising in quadratic curvature gravity minimally coupled to a scalar field. Focusing on the null, weak, strong and dominant energy conditions, we perform a systematic analysis under two distinct formulations of the energy–momentum tensor. In the first approach, the energy–momentum tensor is assumed to be sourced solely by the scalar field, whereas in the second, an effective energy–momentum tensor is constructed that incorporates the higher-curvature corrections characterizing deviations from general relativity. Our results reveal that, in the scalar-field description, the null, weak and dominant energy conditions remain satisfied throughout the cosmological evolution, while the strong energy condition is necessarily violated during the bounce phase, enabling the avoidance of the initial singularity. In contrast, when the effective energy–momentum tensor is considered, all four energy conditions are violated near the bounce, highlighting the intrinsically non-Einsteinian nature of the underlying gravitational dynamics. These findings clarify the role of higher-order curvature terms in facilitating nonsingular cosmological bounces, providing important insights into the energy condition violations required in modified theories of gravity.