Redshift-space distortion from dynamical dark energy with time-dependent Lagrangian perturbation theory

We apply the Lagrangian perturbation theory with time-dependent growth functions at second and third order of perturbation with the aim to model the effect of dynamical dark energy on redshift-space distortions. Our fiducial galaxy redshift surveys are modeled after the upcoming SKA and DESI redshift surveys. We include PLANCK CMB priors and the 20% uncertainty on the linear bias parameter, incorporating the unknown instrumentation noise. After the marginalizing, our results show that the constraints on the density parameter could potentially get better than $\sim$1%, while the constraints on $w_0$ and $w_{\mathrm{a}}$ could be better than $\sim 5\mathrm{\%}$ and $\sim 60\mathrm{\%}$ respectively, consistent with works done before. However, the inclusion of time-dependent growth functions would alter the nonlinear power spectrum by as much as $\sim$10%. The inclusion of the time-dependent growth functions become crucial as the precision gets better.