Model-independent reconstruction of the linear anisotropic stress η

In this work, we use recent data on the Hubble expansion rate H(z), the quantity f sigma(8)(z) from redshift space distortions and the statistic E-g from clustering and lensing observables to constrain in a model-independent way the linear anisotropic stress parameter eta. This estimate is free of assumptions about initial conditions, bias, the abundance of dark matter and the background expansion. We denote this observable estimator as eta(obs). If eta(obs) turns out to be different from unity, it would imply either a modification of gravity or a non-perfect fluid form of dark energy clustering at sub-horizon scales. Using three different methods to reconstruct the underlying model from data, we report the value of eta(obs) at three redshift values, z = 0.29, 0.58, 0.86. Using the method of polynomial regression, we find eta(obs) = 0.57 +/- 1.05, eta(obs) = 0.48 +/- 0.96, and eta(obs) = -0.11 +/- 3.21, respectively. Assuming a constant eta(obs) in this range, we find eta(obs) = 0.49 +/- 0.69. We consider this method as our fiducial result, for reasons clarified in the text. The other two methods give for a constant anisotropic stress eta(obs )= 0.15 +/- 0.27 (binning) and eta(obs )= 0.53 +/- 0.19 (Gaussian Process). We find that all three estimates are compatible with each other within their 1 sigma error bars. While the polynomial regression method is compatible with standard gravity, the other two methods are in tension with it.