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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62 , Issue 9 : 999811(2019) https://doi.org/10.1007/s11433-019-9373-0

Non-parametric reconstruction of growth index via Gaussian processes

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  • ReceivedJan 20, 2019
  • AcceptedFeb 21, 2019
  • PublishedApr 29, 2019
PACS numbers

Abstract

The accelerated cosmic expansion could be due to dark energy within general relativity (GR), or modified gravity. Differentiating between them using both the expansion history and growth history has attracted considerable attention. In the literature, the growth index $\gamma$ has been found useful to distinguish these two scenarios. This work aims to consider the non-parametric reconstruction of the growth index $\gamma$ as a function of redshift $z$ from the latest observational data as of July 2018 via Gaussian processes. We found that $f(R)$ theories and dark energy models within GR (especially $\Lambda$CDM) are inconsistent with the results in the moderate redshift range far beyond $3\sigma$ confidence level. A modified gravity scenario different from $f(R)$ theories is favored. However, these results can also be due to other non-trivial possibilities in which dark energy models within GR (especially $\Lambda$CDM) and $f(R)$ theories may still survive. In all cases, our results suggest that new physics is required.


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11575022, and 11175016). We thank the anonymous referee for useful comments and suggestions, which helped us to improve this work. We are grateful to Hua-Kai Deng, Xiao-Bo Zou, Da-Chun Qiang, Zhong-Xi Yu, and Shou-Long Li for kind help and discussion.


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  • Figure 1

    (Color online) The reconstructed $f\sigma_8$, $\delta/\delta_0$, $\delta^\prime/\delta_0$ and $f$ as functions of redshift $z$, by using Gaussian processes with the squared exponential covariance function. The mean and $1\sigma$, $2\sigma$ uncertainties are indicated by the blue solid lines and the shaded regions, respectively. The observational $f\sigma_{8,\,\text{obs}}$ data with error bars are also plotted in (a). See the text for details.

  • Figure 2

    (Color online) The same as in Figure 1, except for the Matérn ($\nu=9/2$) covariance function. See the text for details.

  • Figure 3

    (Color online) The reconstructed $E$, $E^\prime$, $\Omega_m$ and $w$ as functions of redshift $z$, by using Gaussian processes with the squared exponential covariance function, from the observational $H(z)$ data with $H_0=(67.36\pm~0.54)$ km/s/Mpc. The mean and $1\sigma$, $2\sigma$ uncertainties are indicated by the blue solid lines and the shaded regions, respectively. The observational $E_{\text{obs}}$ data with error bars are also plotted in (a). $w=-1$ is indicated by a red dashed line. See the text for details.

  • Figure 6

    (Color online) The same as in Figure 3, except for the Matérn ($\nu=9/2$) covariance function, and $H_0(=73.52\pm~1.62)$ km/s/Mpc. See the text for details.

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