Exploring Late-Time Cosmology in f (Q) Gravity with Minimally and Nonminimally Coupled Dark Sectors

<div> <span><span> </span>We investigate the viability of modified gravity models based on the nonmetricity scalar $Q$, focusing on cosmologies where both matter and dark energy sectors are either minimally or nonminimally coupled within the framework of $f(Q)$ gravity. Using a generalized action with power-law forms $f_1(Q) = -\alpha Q^2$ and $f_2(Q) = 1$ (minimal) or $f_2(Q) = -\beta Q$ (nonminimal), we study the resulting cosmic dynamics in a spatially flat FLRW universe.&nbsp;</span> </div> <div> <span><span> </span>Using three commonly studied parametrizations of the dark energy equation of state (EoS)---CPL, JBP, and BA---we constrain the model parameters by applying a \(\chi^2\)-minimization method to combined observational data from the Pantheon Type Ia Supernova sample, the latest baryon acoustic oscillation (BAO) measurements from Dark Energy Spectroscopic Instrument second Data Release (DESI DR2), and the cosmic microwave background (CMB) observations.</span> </div> <div> <span><span> </span>By fixing the present values of the matter density parameter $\Omega_{\rm m0}$, Hubble parameter $H_0$, and deceleration parameter $q_0$, we reduce the free parameter space and derive best-fit values for the dark energy parameters $w_0$ and $w_1$.&nbsp;</span> </div> <div> <span><span> </span>Our results show that, in the minimally coupled scenario, cosmic acceleration can be achieved with a smaller dark energy density than in the standard $\Lambda$CDM model, owing to dominant geometric contributions from the nonmetricity scalar $Q$. In contrast, the nonminimally coupled scenario requires a significantly larger dark energy component---approximately $\Omega_{\mathrm{de0}} \simeq 0.66$ for the CPL parametrization and $\Omega_{\mathrm{de0}} \simeq 0.99$ for the JBP and BA parametrizations. The contribution of the nonmetricity sector to cosmic expansion is negative in the CPL case, but weakly positive for the JBP and BA cases. In both coupling regimes, the effective equation of state exhibits phantom-like behavior ($w_0 &lt; -1$). The transition redshift between decelerated and accelerated expansion also differs between the two coupling scenarios, highlighting the influence of nonminimal interactions on cosmic dynamics.</span> </div>