A new parametric observational study of $f(Q,B)$ gravity with modified chaplygin gas

In this work, we explore the cosmological dynamics of a modified gravity framework based on the function $f(Q,B)=\delta Q^2+\beta B$, where $Q$ denotes the nonmetricity scalar and $B$ is the boundary term that relates $Q$ to the Ricci scalar. The matter sector is modeled using the Modified Chaplygin Gas (MCG) with the equation of state $p=A\rho -\frac{B}{{\rho }^{\alpha }}$, allowing the model to interpolate between early-time matter behavior and late-time cosmic acceleration. By deriving an analytical expression for the Hubble parameter $H(z)$, we perform a parameter estimation using Markov Chain Monte Carlo (MCMC) techniques in conjunction with the latest cosmological observations: $46$ Hubble parameter measurements, $15$ BAO data points, DESI DR2 BAO data and the Pantheon+ Type Ia supernovae compilation. The best-fit values are obtained as $H_0=72.22_{-4.46}^{+3.64}$, $A_s=0.696_{-0.129}^{+0.082}$, $\alpha =0.0029_{-0.021}^{+0.022}$, and $A=0.0038_{-0.047}^{+0.071}$. The deceleration parameter transitions at redshift $z_{tr}\approx 0.946$, while the present-day value is $q_0=-0.789$. The model yields an age of the Universe $t_0\approx 13.53$ Gyr and a present EoS parameter ${\omega }_0\approx -0.691$, which reflects the late-time acceleration consistent with observational bounds. These results demonstrate that the MCG scenario within $f(Q,B)$ gravity provides a viable and observationally consistent framework for explaining the late-time accelerated expansion of the Universe.