Suppressing structure growth with Einstein-Aether gravity: A designer approach

Recent large-scale structure observations indicate a lower amplitude of matter density fluctuations than predicted by standard ΛCDM cosmology, motivating the investigation of physical mechanisms that suppress late-time structure growth. In this work, we study linear matter perturbations in generalized Einstein-Aether gravity using a designer approach. We reconstruct the functional form of the Aether Lagrangian, F(K), from pre-specified background expansion histories with both constant and time-dependent dark sector equations of state. This inverse-engineering procedure decouples background kinematics from perturbative dynamics, allowing us to isolate the effects of modified gravity on structure growth. We numerically solve the modified growth equations and test theoretical predictions against a compilation of 63 redshift-space distortion (RSD) measurements, incorporating Alcock-Paczynski geometric corrections to eliminate fiducial model dependencies. Phantom-like configurations of the Aether field generate enhanced Hubble friction that suppresses late-time structure growth. Both the constant and time-dependent equation-of-state models yield statistical fits competitive with ΛCDM (ΔAIC ≈ 1.75−2.15), favoring a reduced present-day clustering amplitude of σ8 ≃ 0.74−0.76, consistent with estimates from weak lensing surveys such as KiDS and DES.