Reconstructing the growth index $\gamma$ with Gaussian Processes

Abstract

Alternative cosmological models have been proposed to alleviate the tensions reported in the concordance cosmological model, or to explain the current accelerated phase of the universe. One way to distinguish between General Relativity and modified gravity models is using current astronomical data to measure the growth index $\gamma$, a parameter related to the growth of matter perturbations, which behaves differently in different metric theories. We propose a model independent methodology for determining $\gamma$, where our analyses combine diverse cosmological data sets, namely $\{f(z_i)\}$, $\{[f{\sigma }_8](z_i)\}$, and $\{H(z_i)\}$, and use Gaussian Processes, a non-parametric approach suitable to reconstruct functions. This methodology is a new consistency test for $\gamma$ constant. Our results show that, for the redshift interval $0<z<1$, $\gamma$ is consistent with the constant value $\gamma =0.55$, expected in General Relativity theory, within $2\sigma$ confidence level (CL). Moreover, we find $\gamma (z=0)$ = 0.311 $\pm 0.144$ and $\gamma (z=0)=0.609\pm 0.200$ for the reconstructions using the $\{f(z_i)\}$ and $\{[f{\sigma }_8](z_i)\}$ data sets, respectively, values that also agree at a 2$\sigma$ CL with $\gamma =0.55$. Our methodology and analyses can be considered as an alternative approach in light of the current discussion in the literature that suggests a possible evidence for the growth index evolution.

11 pages and 8 figures

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• Measuring the matter fluctuations in the Local Universe with the ALFALFA catalog
• A comprehensive data-driven odyssey to explore the equation of state of dark energy
• Is ${\omega }_0{\omega }_a$CDM a good model for the clumpy Universe?
• Viability of general relativity and modified gravity cosmologies using high-redshift cosmic probes
• Probing the Cosmic Distance Duality Relation via Non-Parametric Reconstruction for High Redshifts
• Revisiting the temperature evolution law of the CMB with gaussian processes
• Scalar perturbation and density contrast evolution in $f(Q,C)$ gravity
• Testing Scale-Dependent Suppression of Structure Growth in the Linear Regime