Reconstructing the expansion history of the Universe from type Ia supernovae data, we fit the growth rate measurements and put model-independent constraints on some key cosmological parameters, namely, $Omega_mathrm{m},gamma$, and $sigma_8$. The constraints are consistent with those from the concordance model within the framework of general relativity, but the current quality of the data is not sufficient to rule out modified gravity models. Adding the condition that dark energy density should be positive at all redshifts, independently of its equation of state, further constrains the parameters and interestingly supports the concordance model.
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