Large scale structure constraints and matter power spectrum in f (Q, L₌) gravity

In the present work, we take into account the dynamical system analysis to investigate the matter power spectrum within the framework of the f (Q, L₌) gravitational theory. After obtaining autonomous dynamical system variables for two different particular pedagogical choices of f (Q, L₌) models (A and B), we derive the full system of perturbation equations using the 1+3 covariant formalism to study the matter fluctuations. We present and solve the energy density perturbation equations to obtain the energy density contrast, which decays with redshift for both models for a particular choice of model parameters. After obtaining the numerical results of the density contrast, we computed the matter spectra for each model and conducted a comparative analysis with the ΛCDM. Furthermore, by employing the Markov Chain Monte Carlo (MCMC) analysis, the model parameters were constrained using a combination of different observational data sets to improve the robustness and accuracy of the parameter estimation. Our results indicate that only model A can be compatible with the considered observational data sets.