Energy conditions in \(f(Q, L_m)\) gravity

We are experiencing a golden age of experimental cosmology, with exact and accurate observations being used to constrain various gravitational theories like never before. Alongside these advancements, energy conditions play a crucial theoretical role in evaluating and refining new proposals in gravitational physics. We investigate the energy conditions (WEC, NEC, DEC, and SEC) for two \(f(Q, L_m)\) gravity models using the FLRW metric in a flat geometry. Model 1, \(f(Q, L_m) = -\alpha Q + 2L_m + \beta \), features linear parameter dependence, satisfying most energy conditions while selectively violating the SEC to explain cosmic acceleration. The EoS parameter transitions between quintessence, a cosmological constant, and phantom energy, depending on \(\alpha \) and \(\beta \). Model 2, \(f(Q, L_m) = -\alpha Q + \lambda (2L_m)^2 + \beta \), introduces nonlinearities, ensuring stronger SEC violations and capturing complex dynamics like dark energy transitions. While Model 1 excels in simplicity, Model 2’s robustness makes it ideal for accelerated expansion scenarios, highlighting the potential of \(f(Q, L_m)\) gravity in explaining cosmic phenomena.