Stability and wave dynamics in polytropic Eddington-inspired Born-Infeld gravitating solar plasmas

We investigate the influence of nonlinear gravity corrections, arising from the Eddington-inspired Born-Infeld (EiBI) theory on wave dynamics, stability, and energy transport processes in polytropic, viscous, and turbulent solar plasmas. Analytical and numerical analyses of the Jeans-normalized quadratic dispersion relation demonstrate that both the EiBI gravity parameter $(\chi)$ and the relative polytropic sound speed $(\beta)$ independently regulate oscillation frequencies, growth rates, phase velocities, perturbation energy partitioning, and outward acoustic energy flux. Positive $\chi$ systematically elevates oscillation frequencies, phase velocities, and outward energy flux level by $\sim$10% relative to the Newtonian predictions, while larger $\beta$ enhances them by up to 55%, thereby promoting wave propagation and efficient acoustic transport. Conversely, negative $\chi$ strengthens gravitational binding and increases damping rates by $\sim$40%, particularly for the \textit{g}-modes. Energy partitioning analyses reveal that the EiBI corrections fundamentally restructure the kinetic-electrostatic-gravitational energy balance. While the Newtonian gravity contributes negligibly ($<$4%), nonzero $\chi$ channels up to one-third of oscillation energy into gravitational modes. The modal surface flux calculations further confirm that only the \textit{p}-modes drive outward energy transport (amplification for $\chi>0$, suppression for $\chi<0$). A direct comparative analysis with four years of SDO/HMI Doppler velocity observations demonstrate a robust theoretical agreement for $\chi=3\times10^7$ m$^5$kg$^{-1}$s$^{-2}$, providing the first empirical constraint on the solar EiBI gravity through helioseismology. The findings offer a rigorous framework for advancing our understanding about solar plasma stability, helioseismic signatures, and ambient atmospheric energy transport processes.