Addressing S_8 and H_0 Tensions via Conformal Attractor in Horndeski Gravity: Stability and GW Predictions

This technical note investigates a minimal Effective Field Theory (EFT) mechanism within Horndeski gravity to mitigate the persistent S_8 and H_0 tensions. By employing the matter-tracking ansatz \alpha_M = \alpha_B = 2\beta\Omega_m(a), we introduce late-time cosmological friction and modified gravitational wave (GW) propagation. Under the assumption of a background expansion close to \LambdaCDM, we demonstrate that for \beta = 0.15, the model predicts a 2.80% attenuation in GW signals at z=0.5, providing a distinctive signature for future standard siren observations (LISA/Einstein Telescope). The model is shown to be theoretically viable, respecting \alpha_T = 0 and ensuring scalar stability (c_s^2 > 0).