Model-independent reconstruction of the linear anisotropic stress $\eta$
  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 $\eta_{{\rm
obs}}$. If $\eta_{{\rm obs}}$ 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 $\eta_{{\rm
obs}}$ at three redshift values, $z=0.29, 0.58, 0.86$. Using the method of
polynomial regression, we find $\eta_{{\rm obs}}=0.57\pm1.05$, $\eta_{{\rm
obs}}=0.48\pm0.96$, and $\eta_{{\rm obs}}=-0.11\pm3.21$, respectively. Assuming
a constant $\eta_{{\rm obs}}$ in this range, we find $\eta_{{\rm
obs}}=0.49\pm0.69$. We consider this method as our fiducial result, for reasons
clarified in the text. The other two methods give for a constant anisotropic
stress $\eta_{{\rm obs}}=0.15\pm0.27$ (binning) and $\eta_{{\rm obs}}=0.53 \pm
0.19$ (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.
