Sweeping Horndeski canvas: new growth-rate parameterization for modified-gravity theories
Yuewei Wen, Nhat-Minh Nguyen, Dragan Huterer
Abstract
Abstract We propose and numerically validate a new fitting formula that is sufficiently accurate to model the growth of structure in Horndeski theories of modified gravity for upcoming Stage IV and V large-scale structure surveys. Based on an analysis of more than 18,000 Horndeski models and adopting the popular parameterization of the growth rate f ( z ) = Ω M ( z ) γ , we generalize the constant growth index γ to a two-parameter redshift-dependent quantity, γ ( z ), that more accurately fits these models. We demonstrate that the functional form γ ( z ) = γ 0 + γ 0 z 2 /(1 + z ) improves the median χ 2 of the fit to viable Horndeski models by a factor of ∼ 40 relative to that of a constant γ , and is sufficient to obtain unbiased results even for precise measurements expected in Stage IV and V surveys. Finally, we constrain the parameters of the new fitting formula using current cosmological data.