Observational Constraints On the Growth Index Parameters in f(Q)$f(Q)$ Gravity

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Abstract In this study, the authors analyze constraints on the growth index of matter perturbations, , within the framework of gravity, using recent cosmological observations, at the background and the perturbation levels, including , Cosmic Chronometer (CC), and Redshift Space Distortion (RSD) datasets. The analysis focuses on quantifying the distortion parameter, which measures the deviation of the gravity model from the concordance CDM cosmology at the background level. Specifically, two cases of the growth index parameter are investigated: a constant and a time‐varying . The various parametrizations of the growth index are investigated, expressed as , where the function assumes different forms, including constant (), Taylor expansion around (), Taylor expansion around the scale factor (), and an exponential form (). By employing the Akaike Information Criterion and Bayesian Information Criterion, authors find that the combined + CC+ RSD datasets impose stringent constraints on the value of the growth index. For the model, the results indicate that within the concordance CDM model, is constrained to , showing strong agreement with the theoretical expectation of . However, within the framework of gravity, authors find , which is in a good agreement within errors of the CDM (with a difference of 0.18). Furthermore, when considering a time‐varying growth index, the analysis reveals that the range of spans from 0.596 to 0.62 across the models. Finally, authors compare the obtained results for the growth index parameters within with those from previous studies on modified gravity theories, such as and .

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