Model-independent reconstruction of the linear anisotropic stress $\eta$

TL;DR

This paper develops a model-independent method to estimate the linear anisotropic stress parameter  from cosmological data, testing deviations from standard gravity without assuming specific models.

Contribution

It introduces three novel, model-independent reconstruction methods to estimate  from observational data, providing new constraints on gravity modifications or dark energy clustering.

Findings

All methods produce estimates compatible within 1 error bars.

Polynomial regression results are consistent with standard gravity.

Other methods suggest potential deviations from standard gravity.

Abstract

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.