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We consider the problem of parametrizing modified gravity theories thatinclude an additional vector field in the sub-Hubble regime within thequasi-static approximation. We start from the most general set of second orderequations for metric and vector field perturbations and allow for both temporaland spatial components of the background vector field. We find that in the casein which dark matter obeys standard conservation equations, eight parametersare needed to fully characterize the theory. If dark matter vorticity can beneglected, the number of independent parameters is reduced to four. In additionto the usual scale and redshift dependence, the effective parameters have anadditional angular dependence induced by the preferred direction set by thebackground vector. In the considered sub-Hubble regime, we show that thisangular dependence appears only through even multipoles and generatesanisotropies in the growth function which translate into anisotropies in thegalaxy and lensing convergence power spectra. The angular dependence generatedby the preferred direction is different from that induced by redshift spacedistortions and could be disentangled in the data collected by future galaxysurveys.

Parametrizing modified gravities with vector degrees of freedom: anisotropic growth and lensing