Model-independent reconstruction of the linear anisotropic stress $η$

Ana Marta Pinho, Santiago Casas, Luca Amendola

Published 2018-04-30Version 1

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 a model-independent estimation of the linear anisotropic stress parameter $\eta$. This estimate is free of assumptions about initial conditions, bias and the abundance of dark matter. 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 $\eta_{{\rm obs}}=0.44\pm0.92$, $\eta_{{\rm obs}}=0.42\pm0.89$, and $\eta_{{\rm obs}}=-0.14\pm3.01$, respectively. Assuming a constant $\eta_{{\rm obs}}$ in this range, we find $\eta_{{\rm obs}}=0.405\pm0.63$. We consider this as our fiducial result, for reasons clarified in the text. The other two methods give for a constant anisotropic stress $\eta_{{\rm obs}}=0.205\pm1.37$ (binning) and $\eta_{{\rm obs}}=0.557\pm0.18$ (Gaussian Process). We find that all three estimates are compatible with each other within their $1\sigma$ error bars and compatible with a standard GR value of $\eta=1$, except for the Gaussian Process method.