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 (χ) and the relative polytropic sound speed (β) independently regulate oscillation frequencies, growth rates, phase velocities, perturbation energy partitioning, and outward acoustic energy flux. Positive χ systematically elevates oscillation frequencies, phase velocities, and outward energy flux level by ∼10% relative to the Newtonian predictions, while larger β enhances them by up to 55%, thereby promoting wave propagation and efficient acoustic transport. Conversely, negative χ strengthens gravitational binding and increases damping rates by ∼40%, particularly for the 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 χ channels up to one-third of oscillation energy into gravitational modes. The modal surface flux calculations further confirm that only the p modes drive outward energy transport (amplification for χ>0, suppression for χ<0). A direct comparative analysis with four years of SDO/HMI Doppler velocity observations demonstrates a robust theoretical agreement for χ=3×10^{7}m^{5}kg^{-1}s^{-2}, providing an empirical constraint on the solar EiBI gravity through helioseismology. These findings establish a rigorous framework for testing modified gravity theories and for advancing our understanding about solar plasma stability, helioseismic signatures, and ambient atmospheric energy transport processes.