Observational signatures of scalar field dynamics in modified $f(Q,L_m)$ gravity

Abstract

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 ${\rho }_{\varphi }={\rho }_{c0}\tanh (A+Bz)$. 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 $H_0=74.284_{-4.275}^{+4.155}$, ${\Omega }_{m0}=0.326_{-0.072}^{+0.093}$ 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.

20 pages, 10 figures