{
  "id": "1805.00027",
  "version": "v1",
  "published": "2018-04-30T18:00:03.000Z",
  "updated": "2018-04-30T18:00:03.000Z",
  "title": "Model-independent reconstruction of the linear anisotropic stress $η$",
  "authors": [
    "Ana Marta Pinho",
    "Santiago Casas",
    "Luca Amendola"
  ],
  "comment": "17 pages, 4 figures, 8 tables",
  "categories": [
    "astro-ph.CO",
    "gr-qc"
  ],
  "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 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-30T18:00:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "model-independent reconstruction",
      "linear anisotropic stress parameter",
      "constant anisotropic stress",
      "redshift space distortions",
      "gaussian process method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}