# Testing for gravitational preferred directions with galaxy and lensing surveys

## TL;DR

This paper investigates how galaxy and lensing surveys can detect preferred directions in gravity, using a model-independent approach to identify potential deviations from isotropy in the universe's structure.

## Contribution

It introduces a framework with four effective parameters to analyze preferred directions in gravity and forecasts the sensitivity of future surveys to these modifications.

## Key findings

- Future Euclid-like surveys can detect preferred directions in gravity.
- The framework distinguishes between effects of preferred directions and primordial isotropy violations.
- Multipole spectra are sensitive probes for anisotropic gravitational interactions.

## Abstract

We analyze the sensitivity of galaxy and weak-lensing surveys to detect preferred directions in the gravitational interaction. We consider general theories of gravity involving additional vector degrees of freedom with non-vanishing spatial components in the background. We use a model-independent parametrization of the perturbations equations in terms of four effective parameters, namely, the standard effective Newton constant $G_{eff}$ and slip parameter $\gamma$ for scalar modes and two new parameters $\mu_Q$ and $\mu_h$ for vector and tensor modes respectively, which are required when preferred directions are present. We obtain the expressions for the multipole galaxy power spectrum in redshift space and for the weak-lensing shear, convergence and rotation spectra in the presence of preferred directions. By performing a Fisher matrix forecast analysis, we estimate the sensitivity of a future Euclid-like survey to detect this kind of modification of gravity. We finally compare with the effects induced by violations of statistical isotropy in the primordial power spectrum and identify the observables which could discriminate between them.