We investigate the cosmological implications of a tanh-parametrized scalar field model in the framework of modified $f(Q, L_{ m})$ gravity by adopting the form $f(Q, L_{ m})=\beta Q+\delta L_{ m}$ along with a scalar field energy density $\rho_\phi = \rho_{ c0} \tanh(A + Bz)$. Using MCMC methods and combining $31$ cosmic chronometer data points, $15$ BAO, DESI DR2 BAO and $1701$ Pantheon+ samples, we constrain the model parameters and obtain $H_{ 0}=74.284^{ +4.155}_{ -4.275}$, $\Omega_{ m0}=0.326^{ +0.093}_{ -0.072}$ and $B=-0.001^{ +0.030}_{ -0.030}$. The model predicts a transition redshift $z_{ tr}=0.5914$ and a present deceleration parameter $q_0=-0.5167$, consistent with a Universe transitioning from deceleration to acceleration. We further analyze the evolution of the EoS parameter, density components and statefinder diagnostics in which all parameters show asymptotic convergence to a de Sitter phase. Additionally, we study black hole mass accretion, showing its dependence on the scalar field dynamics. This work highlights the compatibility of tanh-scalar field forms with $f(Q, L_m)$ gravity in describing cosmic acceleration and gravitational phenomena.
Categories: gr-qc hep-th