Revisiting the S 8 Gap: Non‐Metricity in Light of DESI DR2 and Gravitational Wave Standard Sirens

ABSTRACT The model faces persistent discrepancies between early‐ and late‐Universe measurements of the Hubble constant () and matter clustering (). We investigate whether the metric‐affine framework of symmetric teleparallel gravity can accommodate these tensions. Constraining the reciprocal model with DESI DR2 BAO, Pantheon+ Supernovae, and RSD data, our joint MCMC analysis reveals a mild preference for a negative geometric density parameter (). Within the reciprocal framework, such values modify the late‐time growth history through a reduction of the effective gravitational coupling, yielding an intermediate clustering amplitude () that accommodates the tension. Conversely, the model does not intrinsically shift using uncalibrated low‐redshift geometric data ( km ), though high‐ solutions remain compatible when local SH0ES calibrations are included. Finally, we forecast the constraints from future Einstein telescope and LISA standard sirens. By probing the non‐metricity sector via modified wave propagation, future sirens could reduce uncertainties to sub‐percent levels ( km ) conditional on specific astrophysical assumptions, while placing significantly tighter constraints on deviations from general relativity.